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No. 4 ''^-i^ J5 



DETERMINATION OF THE PARALLAXES OF FIFTY 
STARS, AND DESCRIPTION OF THE INSTRU- 
MENTS AND OF THE METHODS EMPLOYED 



By 
JOHN A. MILLER 

ASSISTED BV 

SAMUEL G. BARTON, HANNAH B. STEELE 

AND 

JOHN H. PITMAN 



/ 

PRINTED BY J. B. LIPPINCOTT COMPANY, PHILADELPHIA 



No. 4 



DETERMINATION OF THE PARALLAXES OF FIFTY 
STARS, AND DESCRIPTION OF THE INSTRU- 
MENTS AND OF THE METHODS EMPLOYED 



JOHN A™ILLER 

ASSISTED BY 

SAMUEL G. BARTON, HANNAH B. STEELE 

AND 

JOHN H. PITMAN 



PRINTED BY J. B. LIPPINCOTT COMPANY, PHILADELPHIA 



QB?/3 
Ms 



DETERMINATION OF THE PARALLAXES 

OF FIFTY STARS, AND DESCRIPTION 

OF THE INSTRUMENTS AND OF 

THE METHODS EMPLOYED 

INTRODUCTION. 

The major part of the observing energ}- of the staff of the 
Sproul Observatory has for some time been devoted to the de- 
termination of Stellar Parallax. I have given in the following 
pages a brief description of the instruments used, the methods of 
observing and reduction that have been employed, and the results, 
together with the data of observation and measurement, for fifty 
stars. 

These results have been obtained through the efforts of sev- 
eral persons. The work has been prosecuted according to plans 
outlined by the writer. Associated with him at various times 
have been Dr. Samuel G. Barton. Hannah B. Steele, John H. 
Pitman, and the Reverend \\'alter A. ]\Iatos. Doctor Barton, 
Mr. Pitman, and the writer have given during the time the work 
was in progress the major part of their efforts to other college 
duties, each having had a comparatively heavy teaching roster. 
Miss Steele also had some other college duties. 

Doctor Barton was at the observatory two years, 1911-1913, 
in the beginning, and had a very considerable part in the prelimi- 
nary adjustments of the telescope and in the determination and 
elimination of the errors of the telescope and measuring engine. 
'Mr. Pitman came to the observatory in 191 3, when Doctor Barton 
went to the Flower Observatory, and has been here ever since. 
In addition to the routine of making exposures and measures, he 
has had a large part in the selection of the observing program and 
methods of procedure. i\Iiss Steele has spent three years here, 
and during that time has reduced practically all measures, has 
made many of the exposures and measured many of the plates. 
Doctor ]\Iatos has been a voluntary observer for a little more than 
a year. I have endeavored in the following pages to give as 



2 JOHN A. MILLER 

nearly as can be done due credit for each specific piece of work, 
using the proper initials in the body of the text. We have con- 
sulted freely and frankly, and changes that have been made in 
our methods at any time were likely to result from the suggestion 
of any one of us. It is a pleasure to acknowledge the whole- 
hearted cooperation of every one working at the problem. 

PART I. 

The Telescope and Accessories. 

The Telescope: Its Objective. — The telescope used in mak- 
ing the observations is a visual refractor of 24 inches aperture 
and approximately 433 inches focal length. It is the major in- 
strument of the equipment given to Swarthmore College by Wil- 
liam Cameron Sproul, a graduate of the college of the class of 
1891. 

In May, 1907, the college entered into a contract with the 
John A. Brashear Company, Limited, to furnish the entire equip- 
ment provided for by Mr. Sproul. The 24-inch telescope was 
completed and mounted in its observatory in December, 191 1, the 
long delay being due to a somewhat tedious wait of four years 
for disks out of which the lens could be constructed. The order 
for these disks was placed by the Brashear Company early in 
1907 with the Parra-Mantois Cie., who, in August, 1909, de- 
livered a crown disk and would have, but for an unfortunate 
accident, delivered a flint disk the same year. Subsequently 
Schott and Gennossen, of Jena, also undertook the manufacture 
for us of a set of 24-inch disks. Both firms produced several 
flint disks which were either broken in annealing or were imper- 
fect because of striae. Finally, in February, 191 1, Schott and 
Genossen delivered a flint disk; accordingly, the objective is 
made of a crown disk by the Parra-]\Iantois Cie., and a flint disk 
made by Schott and Gennossen. Of the quality of these disks Mr. 
McDowell says that every optical test shows both these disks to be 
as nearly perfect as any he has ever examined. 

Soon after the telescope was mounted Prof. R. W. Marriott 
and myself applied to the objective the method of extra focal 
images devised by Hartmann. We covered the objective with a 
screen containing 44 circular holes 33 mm. in diameter. The 
centres of these holes were on nine different zones. With this 



DETERMINATION OF PARALLAXES OF FIFTY STARS 3 

screen we photographed Capella when it was near the meridian, 
photographing through a yellow ray filter, made by Wallace in 
accordance with the color curve of the objective. We used 
Cramer instantaneous isochromatic plates. These plates, when 
measured and reduced, showed the presence of certain small as- 
tigmatic errors that Mr. McDowell asserted were not present in 
the objective when it was in the optical room. He surmised that 
it w^as due to the pressure of a spring used to prevent the objec- 
tive from sliding in its cell. At Mr. McDowell's suggestion we 
repeated the test, after reducing the pressure of this spring, using 
Arcturus instead of Capella, and using a screen containing 78 
circular holes, distributed on ten zones. Notwithstanding the 
fact that Capella was photographed with the telescope east and 
Arcturus with the telescope west of the meridian, that one of 
them was north and the other south of the zenith, that the tem- 
perature was low when Capella was photographed and high when 
Arcturus was photographed, both tests showed qualitatively prac- 
tically the same astigmatic errors, though they were smaller in 
the case of Arcturus than with Capella. These errors are not 
large : in fact, they are very small. \N\th. the values thus ob- 
tained we computed Hartmann's Characteristic T by which he 
measures the quality of an objective. Hartmann said, when he 
devised this method of testing objectives, that if T turned out 
to be less than 0.5. the objective is " preeminently excellent." ^ 
The result which we obtained for the Sproul objective gives T = 
0.27. 

In 19 13 ^ we decided to repeat the Hartmann test of the objec- 
tive, after having again reduced the pressure of the spring re- 
ferred to above ; and in order to cover the lens very completely, 
we decided to use three screens. 

Screen No. i contained ^2 holes, arranged on eight zones ; the 
radii of the zones on this screen were 2, 5, 6.5, 8, 8.75, 9.5, 10.25, 
and II inches, respectively. 

Screen N'o. 2 contained 36 holes, arranged on nine zones ; the 

^ Hartmann : Zeitschrift fiir Instrnmentenkunde , vol. 24. 
Plaskett : Astrophysical lournal, vol. 25. 
Fox : Ihid., vol. 27. 

Hartmann: Pub. des Astro physikaUschen Obs. zu Potsdam, Nr. 46. 
^For details of this test see Sproul Observatory Publications No. 3; The 
Journal of The Franklin Institute, vol. clxxviii, No. 4, October, 1914. 



4 JOHN A. MILLER 

radii of these zones were 2.25, 4.25, 5.25, 7.25, 8.375, 9-i75> 
9.875, 10.625, and 11.375 inches. 

Screen No. j contained 14 holes, arranged on seven zones ; the 
radii of these zones were 1.5, 3, 3.75, 4.5, 5.875, and 7.625 inches. 

On January 9, 191 3, Capella, when near the meridian, was 
photographed through each of these screens in the following 
manner : 

Each screen was used in two positions. Screen No. i was 
set with a given diameter parallel to the equator and five ex- 
posures were made. It was then rotated through 45 degrees about 
an axis through the centre of the lens perpendicular to the plane 
of the screen and five additional exposures made on another 
plate. Screen No. i was then removed and Screen No. 2 placed 
over the lens and, five exposures through it having been made, 
it was turned 45 degrees and five additional exposures made on 
another plate. Screen No. 2 was then removed and Screen No. 3 
put in its place, and, five exposures having been made, it was 
turned through 90 degrees and five exposures made on another 
plate. Integrating these results, this was equivalent to photo- 
graphing through a single screen containing 164 holes, arranged 
on 24 zones. There were eight holes on each of 17 zones and 
four holes on each of seven zones. These holes were distributed 
on diameters of the lens making angles of 22^ degrees with each 
other. Fig. i shows this integrated screen. 

It will be noted (see Fig. i) that some of the holes partially 
overlap each other. The numbers in the holes show the number 
of hundredths of a millimetre that that particular part of the lens 
was in error. The heavy circles represent the positions in which 
the lens focused too short, and the light circles where it focused 
too long. 

We used every precaution possible to eliminate local errors. 
The screens had been in the dome-room for several hours previ- 
ous to making the photographs in order that they might be of the 
same tem^perature as the lens. The screens were constructed 
carefully and oriented so that the centre of the screen was super- 
imposed on the centre of the objective. Each set of five ex- 
posures was made on the same plate. The first exposure was in 
the centre of the plate and the remaining four grouped sym- 
metrically around the centre one, displaced just' enough so that 
their patterns did not overlap each other. The plates were then 
measured on a measuring engine, one set each by Prof. S. G. 



DETERMINATION OF PARALLAXES OF FIFTY STARS 5 

Barton, Professor Marriott, and myself. The agreements be- 
tween the measures are satisfactorily accordant. 

The curves in Fig. 2 are the curves of zonal error ; the abscissa 
of any point is the radius of a zone, and the corresponding ordi- 
nate is the focal length of that zone diminished by a constant 
and multiplied by 25, so that the difference of any two ordinates 

Fig. I. 




is 25 times the difference in the focal length of the two corre- 
sponding zones; that is, the errors are magnified 25 times. The 
actual difference between the greatest and least focal length of 
any two zones is less than i.i mm. The curves EF ^ CD, and AB 
are respectively the graphs of the measures made by Miller and 
Marriott, and the mean of those measures. Barton did not meas- 
ure one of the plates in the series. For this reason his measures 
were not included, in the computation of the zonal error. 



JOHN A. MILLER 



Hartmann's characteristic quantity, 
his formula : 



T/^ was computed by 



T = 



100,000 ^rd 



200,000 '^r'^iAn — Ao) 

n = I 



F 2r F^^r 

where F is the focal length of the objective, r the radius of a zone, 
d the diameter of a circle of confusion, An the focal distance of 
the zone n, and Ao the quantity determined by the Hartmann 
formula. 

We found : 

T=^.o68 from Marriott's measures, and 
T=.o86 from Miller's measures. 

We also computed the diameters of the circles of confusion 
for each of the 24 zones. Expressed in terms of hundred thou- 
sandths of the focal length, the diameter of the maximum circle 
of confusion was 0.143. 

Fig. 2. 



^r^ 


rf 


\ 


<\ 


^ 


FY 


nrmv-r-n-r-f 


c^ 




N 


n 


-^ 


1 


1 1 lV>n~.° 


'^ 


~i\ 


\ 








iTTrT — r-. . _ B 


■ J- ITmTTi n R 



The curve of zonal error. The error is magnified 25 times. 

These tests show that the lens is an excellent one, the focal 
discrepancies, the diameters of the circles of confusion, and T, 
the weighted diameter of confusion, all being extremely small. 

The mounting of the telescope, also by the Brashear Com- 
pany, is described at some length in Sproul Observatory Publi- 
cation No. 2 and in Popular Astronomy, vol. xxi. No. 5, May, 

1913- 

Double-slide Plate Holder. — We are determining stellar paral- 
laxes by means of photography, following with very slight modi- 
fications, which are pointed out later, the method described in the 
Astrophysicai Journal, vols. 32, 33, and 34, by- Schlesinger. 

The telescope is provided with a double-slide plate holder es- 



DETERMINATION OF PARALLAXES OF FIFTY STARS 7 

sentially the same as that designed by Ritchey, and described by 
him in the Astrophysical Journal, vol. 12, p. 355. A screw placed 
convenient to the operator serves to move the plate holder in 
right ascension, and one at right angles to it to move it in declina- 
tion. The screws originally provided were somewhat unsatis- 
factory. To adjust them so that there was no lost motion and so 
that the operator could move them easily was a tedious cut-and- 
try process. It seemed also that the wearing of the material and 
the changes of temperature of the instrument easily led to malad- 
justment, the result being that the operator often worked when 
the adjustment was not perfect, and, in the beginning at least, 
these screws contributed more than their share to the making of 
bad images. We afterward had these screws replaced by others 
designed and made by R. Pietsch and Company, 830 Race Street, 
Philadelphia. They are made as follows : The stem on which 
the screw is cut is of stiff, hard steel. The end of the stem 
farthest from the grip by which the observer turns the screw 
terminates in a sphere which is enclosed in a spherical bearing, 
which is concentric with the sphere on the end of the stem. This 
spherical bearing can be adjusted by means of a nut so that the 
sphere rotates easily in its bearing with no perceptible lost mo- 
tion. This bearing is fastened to the box carrying the plate 
holder. The screw passes through a cylindrical nut, split along- 
one element of the cylinder, which is fastened to the frame of the 
telescope. Approximately perfect adjustment is easily made by 
means of a screw through a flange containing the element, and 
when once made is reasonably permanent. 

Ray Filters. — Since the objective is a visual one, we use a 
ray filter^ transparent to those rays for which the objective is 
focused best. We use one of two filters. One of these was made 
by Wallace and consists of a piece of worked glass covered with a 
thin gelatin film stained with a dye. In order to protect the film, 
the first glass plate is cemented to another plate of worked glass. 
The filter absorbs the rays that it should, but the surfaces of it are 
not optically plane nor are they exactly parallel. Computations 
show that a star image might be displaced 0.0008 mm., due to the 
fact that the surfaces are not plane. This error is smaller than the 
error of bisection, and yet it seemed unwise to deliberately run the 
chance of introducins: it. According^ly, Petitdidier, at my re- 

^ Ritchey : Astrophysical loiirnal, vol. 12, pp. 353, 354. 



8 JOHN A. MILLER 

quest, constructed for us a filter from a single slab of optical 
glass by Schott and Gennossen which is transparent to prac- 
tically the same rays as the Wallace filter is. The faces of this 
filter are parallel planes. We are using plates 5 by 7 inches. It 
was impossible to secure a slab as large as that which was homo- 
geneous in color and structure. This filter is 4^4 by 5 J4 inches. 
The quality of the images made through the tw^o filters as seen 
through the microscope of the measuring engine is about the 
same. If it happens that because of its size the Wallace filter 
gives a more desirable field of comparison stars, we use that filter, 
otherwise we use the Petitdidier filter. The Wallace filter is 
always put in the plate holder in the same way, and, since the 
star images fall at the same place on the filter for all the plates 
oi a given star, it is quite unlikely that any error is introduced by 
its use. All the plates for any one star are taken with the 
same filter. We compared the filters by examining the residuals 
found in reducing the measures. From 259 plates the Wallace 
filter gave an average residual of 0.0064 quarter millimetre. 
From 106 plates the Petitdidier filter gave an average of 0.0062 
quarter millimetre : from which it would appear that one filter 
is as good as the other. 

Plates. 

After some experim.entation with various makes of plates, we 
found the Cramer instantaneous isochromatic plates and the Ham- 
mer orthochromatic plates best suited to our purpose. ]\Iost of 
our negatives have been made on Cramer plates, and we are using 
those at present. 

Tlie Occulting Disk: The Optical Centre. 

It is desirable to have the images of all the stars that are to 
be measured nearh^ the same size. In order to reduce the images 
of the parallax star to the average size of the comparison stars 
we have adopted the occulting device designed by Schlesinger 
and described by him in the Astrophysical Journal, vol. 32, pp. 
384, 385. This occulter is driven by a little toy motor which is 
fastened to the double-slide plate holder. 

We have used this device whenever the parallax star is brighter 
than the eighth magnitude. Wq have reduced stars as bright as 
Procyon to that of a star of ninth magnitude, the width of the 



DETERMINATION OF PARALLANES OF FIFTY STARS g 

sector opening in that case being about t^-q of the entire circum- 
ference. It is possible that in the case of a very narrow opening, 
such as is necessary for Procyon or even for stars of the third 
magnitude, diffraction errors may enter. The entire matter 
should be investigated. So far as residuals indicate in the re- 
duction of the plates, we have not been able to discover any. 
The optical centre of a photograph has been defined as the 
foot of a perpendicular let fall on the photographic plate from the 
centre of the objective. At the very beginning of our work we 
determined the position of this optical centre of the photograph, 
using the method described by Schlesinger.^ Wt found that the 
plane of the plate was not exactly perpendicular to the optical 
axis of the objective and that the error was in the construction 
of the metal plate holder. This error was corrected and the 
optical centre of the photograph redetermined and was found to 
be 0.34 inch north and 0.05 inch east of the geometrical centre 
of the plate. The optical centre was redetermined by Mr. Pit- 
man just recently and found to coincide with the position found 
three years ago. 

Tlie Exposures. 

Our ideal is to expose 12 plates — three plates on each of four 
epochs — on any one region. \\t usually make three exposures 
on each plate and develop it at once. Six of these plates are ex- 
posed at the time of negative parallactic displacement -and six 
at the time of positive parallactic displacement. This has been 
our ideal. Occasionally it is possible to secure only two expos- 
ures on a plate. In a few instances five plates have been made of 
a field when the parallactic displacement is negative (or positive) 
and seven plates when the parallactic displacement is positive 
(or negative), and occasionally we have more than 12 plates, and 
in a few instances only ten plates have been measured. These 
cases are pointed out in the detailed discussion of each star. We 
have (see the discussions of Kapteyn, Schlesinger, Russell, and' 
others) exposed only when the star is near the meridian; never 
when the hour angle is more than one and one-half hours; at the 
end of the exposure; and usually the extreme hour angle is less 
than one hour. All in all, we are a little more likely to have 
western hour angles in our evening observations and eastern 
hour angles in our morning observations. AVith hour angles 
such as we are using the differential refraction does not cause 
* Asfrophysical lournal, vol. 2)'^, p. 376. 



10 JOHN A. MILLER 

appreciable errors, and our residuals do not seem to depend upon 
whether the hour angle is east or west. 

The times of exposures vary from three minutes to twenty 
minutes, the average exposure being about nine minutes. Our 
work at the telescope is as follows : On an observing card we 
have a chart of the region of which the parallax star is the 
centre; its coordinates and its magnitude: the angle that the 
Qccrdter should be opened; the setting of the eye-piece for the 
guiding star ; and the time of the exposure. The parallax star is 
brought to the middle of the field by rneans of a visual eye-piece, 
fastened to a metal plate which is put in a plate holder in the 
place to be occupied by the .photographic plate. All exposures 
have been made with the telescope on the west side of the pier. 

The PrograuL 

The program of observation was selected before the appoint- 
ment of the parallax committee by the American Astronomical 
Society. It was found desirable, after the appointment of this 
committee, to modify it only slightly. At present it includes ob- 
jects found in one of the following named classes. The greater 
emphasis is placed upon the first three classes. 

1. All visual binaries whose orbits are well determined; also 
those visual binaries whose orbits we have reason to believe will 
be determined in the not too distant future. 

2. Some spectroscopic binaries. 

3. Some objects with large hypothetical parallax. 

4. Three or four objects whose parallaxes are well determined 
(intended for calibration of our methods and results). 

5. Some objects of large proper motion. 

6. Objects whose hitherto determined parallaxes are dis- 
cordant. 

7. Some objects of especial interest, such as Nova Geminorum 

11 and Barnard's '' Runaway Star." 

PART II. 

Choice of Comparison Stars. 

In the main we have chosen four or five comparison stars. 
Four, properly distributed, I believe to be all that are necessary. 
In choosing them we have had these ideals : ( i ) They should be 
arranged symmetrically about the parallax star, and (2) they 
should be nearly of the same magnitude, (2) being of much more 



DETERMINATION OF PARALLAXES OF FIFTY STARS ii 

relative importance than ( i ) . This canon has been violated in 
some of our earlier series, but adhered to very strictly in our 
later work. Our first and chief variation from the practices of 
observers preceding us is in our method of choice of comparison 
stars, and I shall nov^ discuss it in some detail. A\^e proceed as 
follows : We choose two of the best plates taken at each of three 
epochs (that is, six plates in all) , and measure the x-coordinates of 
most if not all the stars on them that are about of the same bright- 
ness. The number of stars on the plate, of course, varies with 
the richness of the field. Some plates may have only four stars 
satisfying the conditions, others as many as 15. The largest num- 
ber that we have measured on any one plate is 12. On an aver- 
age w^e measure eight stars preliminary to the final choice of a 
field. Having measured these six plates and chosen one as a 
standard, we compute the orientation factors by formula (3), 
page 2;^ (which see), by which wx can compute from the meas- 
ured x-coordinates the x-coordinates that would have resulted if 
the plate had been set up exactly as the standard plate was and 
under the same temperature conditions. If there be n stars in 
this preliminary field and if X be the x-co6rdinate of the centre 
of gravity of this preliminary field of comparison stars, and Xi 
the x-coordinate of the z'th star of the field on the oriented plate, 

^^^^ X = Mi 

11 

We now refer the stars to this centre of gravity, and write 

X = Xi- Xi 

Let us suppose plates have been measured at each of four epochs, 
and let us consider the /th star. Since no confusion will arise we 
shall not carry the designating subscript / and shall let the sub- 
scripts I, 2, 3, 4 designate the x-coordinates of the same star at 
the respective epochs. 

If now P be the parallax factor, /^ the proper motion relative 
to the centre of gravity, T the time of the observation referred 
to an arbitrary epoch, C a constant, and tt the parallax relative to 
the centre of gravity, we have the equations : 
Xi - X, = xi = Pi- + r," + c, 

X, - X2 = X2 = P2^ 4- T2F- + c, 
X3 - Xs = X3 = Pz^ 4- T,u- + C, 
X, - Z4 = X, = P4- + T,,u + C. 



12 JOHX A. MILLER 

A\'e can determine t? and fj^ from these equations ; for our im- 
mediate purposes it is sufficiently accurate to make the assum.p- 
tion Pi = P. and P. = P^. ' 

:. Xz - Xi = {Ts -Ti)u, 
an^ X2 -xi = {Po - Pi)- + {T2 - T,)u. 

These equations determine tt and /^ of this particular star relative 
to the centre of gravity of this preliminary field. We treat each 
of the stars in a similar manner. This preliminary field is origi- 
nally so chosen that several groupings are possible, each of which 
permits a choice of a final field that satisfies the requirements for 
symmetry and magnitude. In choosing our final field we in gen- 
eral reject those stars that show large positive parallaxes and in- 
clude those that show large negative parallaxes. It seldom hap- 
pens that a preliminary field of eight stars contains more than 
one or two that would be excluded from the final field by this 
method, nor more than about the same number that would cer- 
tainly be included. 

In order to show the relation a little more readily to the eye, 
we graph the results as follows : \A'e plot as many points on 
millimetre paper as there are epochs. To fix the ideas, let us sup- 
pose there are four epochs in the order that the eastern and the 
western parallactic displacements alternate. A\'e then plot 4 
points, 0, A, B, C (see Fig. 3), whose abscissae and ordinates 
are all, respectively, c, 0; T^^-T-^, X^-X-^; Tn-T^, X.-X-^^; T^-T-^, 
X4-X1. It is evident that the ordinate of B is the proper mo- 
tion of this star relative to the centre of gravity; and that the part 
of the ordinate of ^ included between A and a line joining 
and B represents approximately double the parallactic displace- 
ment at that epoch, actually AD represents {P-2-Pi)'^- These are 
plotted in terms of thousandths of a quarter millimetre, and when 
I speak in what immediately follows of a parallax or a proper 
motion of ten I mean that the displacement is o.oio quarter milli- 
metre. We use the fourth epoch (if there be one) as a check. 
It is evident that in general the line joining OB should be parallel, 
or nearty so, to the one joining A and C, and that the line joining 
and A should be parallel to the line joining B and C. The 
graph (or the equations) then give two determinations of the 
parallax and of the proper motion, and hence a chance for com- 
parison and check. We have used four epochs whenever the 



DETERMIXATION OF PARALLAXES OF FIFTY STARS 13 

observations were available. Several questions arise in connec- 
tion with this practice. I shall discuss three of them. 

I. Are the parallaxes of the comparison stars determined in 
this way and which are very small quantities real, or are they 
simply the unavoidable errors of measurement? 

In my judgTiient, the answer to this question is that they are 
real, but not unqualifiedly so, for reasons I shall now state. Or, 
better stated, perhaps the parallaxes thus found, in most instances 
are so small that thev are non-committal, but there are many in- 



^--^B 



-if- 



TigZ 



stances in which they are certainly qualitatively dependable. A\'e 
have discussed in all 25 fields in this way. The parallax of ten 
of these 25 stars had been determined before we devised this 
method, all but one of the ten being visual binaries whose orbits 
were well determined. The average number of comparison stars 
per field for this ten was 4.5. Tzijo of these ten fields showed 
that in each we had chosen for a comparison star one that had 
considerable parallax. In each case this comparison star was 
rejected and the parallax recomputed. The remaining 15 pre- 
liminary fields had an average of eight stars in them : the largest 
number of stars in any one field was eleven and the smallest num- 
ber five. Nine of these fields were graphed at four epochs. The 
points O, A, B, and C w^ere plotted as before described. For all 
those stars, for which the line joining two evening observa- 
tions is parallel to a line joining two morning observations — 
and this is a severe test — we have said the graph checked, but if 
it failed in any particular we counted it as '' not checked." It 



14 JOHN A. MILLER 

might happen that two or three or four or more stars checked and 
the remainder did not. In the case of fields when one plate only at 
each epoch w^as measured there w^ere as many cases that did not 
check as there were that did check. In the cases that all the stars 
of the preliminary field were measured on tzvo plates at each 



Fig. 4. 

epoch the number of " checks " to that of '' not checked " was 
in the ratio of 11 to 5. Judging from these data, we should 
conclude that one plate measured at each epoch would not tell 
us much. But two plates at each epoch do. But the data at 
present are too meagre to justify generalization. The quan- 



DETERMINATION OF PARALLAXES OF FIFTY STARS 15 

titles Xo-^'i, 'I's-'t'i, as well as the parallax of the comparison stars 
on this graph, are given in terms of thousandths of a quarter of 
a millimetre and are usually too small to indicate anything. 

In a field of eight stars there are seldom more than two 
whose parallax is large enough to be a guide. In ten fields 
averaging eight stars to each field there were in all twenty- 
two stars for which the distance AD, which represents roughly 
double the parallax of the star, was ten or greater; that 01 59 
was less than ten. The double parallax of six out of 81 was 
greater than 20. In our choice of the final field we are influenced 
very little by a double parallax of less than eight and not at all 
by one less than five. 

The dift'erences Xo-a'i . . . used in making the graph 
are also usually very small. Wt computed the probable error 
for all the dift'erences for those fields where two plates had been 
measured at each epoch. There were 88 differences numerically 
greater than ten; of these, eight dift'erences had a probable error 
greater than the quantity we were seeking, and in 80 cases the 
probable error was less. Taking all the differences, there were 
about as many probable errors less as there were greater than 
the quantity we were seeking. The sum of all the differences 
w^as just about twice the sum of all the probable errors. The 
nature of the results is fairly illustrated by the case of e Androm- 
edse measured by Miss Steele. Fig. 4 is the graph of e Androm- 
edse and its preliminary field of comparison stars. In the table 
on page 16 the first row contains the number of the star on the 
plate ; the second row the quantity .I'g-.^i for each of the stars ; 
the third row the corresponding probable error ; the fourth row 
the quantity .I'o-.i'i; the fifth row the corresponding probable 
error; the sixth and seventh rows the quantity .Vj^-i'i and corre- 
sponding probable errors. The eighth row contains the double 
parallaxes of each star read from the graph of the first three 
epochs. The ninth row contains the double parallaxes of the 
same stars as read from the graph for the last three epochs. 
By observing the graph it will be noticed that the stars 3, 5, 6, 
7, and 8 " check," and the stars i and 2 do not. A good illus- 
tration of the graph of the star that checks is that of No. 8 and 
parallax. A good illustration of that of a star which does not 
check is No. 2. 



i6 



JOHN A. MILLER 



€ Andromedse 



Star No. 


TT 


1 


2 


3 


5 


6 


7 


8 


Xz-Xi 


30.0 


37-0 


16.0 


lO.O 


8.0 


I.O 


lO.O 


24.0 


p. e. 


44 


2.1 


3.1 


7.1 


7-3 


4-3 


4.1 


1.8 


X3-X1 


64.0 


4.0 


16.0 


4.0 


6.0 


4.0 


1.0 


15.0 


p. e. 


7-7 


9.8 


lO.O 


8.2 


8.8 


5-0 


6.4 


18.6 


X4-.T1 


100. 


5-0 


8.0 


lO.O 


6.0 


20.0 


7.0 


3-0 


p. e. 


3-9 


3-5 


5-3 


7-1 


7.0 


2.1 


3-9 


6.7 


I.Stt 




+40.0 


-6.0 


-8.0 


+4-0 


-4.0 


+9-0 


-34-0 


I.QTT 


+ 14-0 


+31-0 


+3-0 


-6.0 


0.0 


-4.0 


+9.0 


-33-0 



2. The second question is, Do we get nearer the truth in this 
way than we should have done had we chosen the field at 
random ? 

Suppose the parallaxes obtained for these comparison stars 
were due wholly to observational error. Then the effect would 
be to introduce a systematic error into parallax determination. 
For the measures of this preliminary field are just half of all the 
plates measured, and the rejection of any of the stars because 
they show a large positive parallax, and the inclusion of others 
because they show a large negative parallax, prejudice the de- 
termination in favor of large parallaxes. In many cases there 
are no large parallaxes of the comparison stars shown, and hence 
there is no prejudice carried by any field choice, but there are 
cases in which large parallaxes do appear. They are either real 
or due to observational errors. If they are real the large positive 
ones should be rejected and large negative ones included in the 
final field chosen; particularly is this so for the binary stars 
which form so large a part of our program, because the parallax 
enters so directly into the determination of the mass, dimen- 
sions, and luminosity of the system. If, on the other hand, 
these parallaxes determined in this way are spurious, and if the 
large positive ones are rejected and large negative ones included, 
the results will certainly be in error. One might free his results 
from this prejudice by rejecting, for the purpose of determining 
the parallax, the six plates used for the purpose of determining 
the field. This would require that six additional plates should 
be taken, which would increase the photographic work by 50 
per cent. The computation and measurement in such cases 
would be double that required when the fields are chosen at 
random. The errors of observation arise from the error of 



DETERMINATION OF PARALLAXES OF FIFTY STARS 17 

bisection of the images in measuring, the distortion of the film, 
the " guiding " error, and some other causes. The first and 
perhaps least influential of these could be removed from the 
final results by remeasuring the six plates from which the field 
was chosen. Perhaps this should be done. It is hard to believe, 
however, that errors could result in such a way as to make a 
graph built from four epochs " check." 

3. Is all this extra work worth while? 

I believe it is for the program we are carrying here ; for the 
parallax enters so directly into the determination of the mass of 
a binary and the linear dimensions of its orbit, and hence it is 
desirable to get as nearly as possible an absolute parallax. It is 
true that there will be many preliminary fields from which a final 
field can be chosen that carries no prejudice with it because all 
of the parallaxes are small. But in the case of binary stars, if 
a comparison star shows a large positive parallax, it is better to 
take a field without it, and to determine the parallax from plates, 
not measured in choosing the final field. 

A case in point is that of 8 Cygni, for which we had taken 
more than the required number of plates. Six plates with the 
preliminary field of stars numbered i, 2, 3, 6, 7, 9, and 10 showed 
that stars numbered i, 3, and 9 had a rather large positive 
parallax, and that the stars numbered 2, 6, and 10 had a negative 
parallax; star numbered 7 had a very small positive parallax. 
We retained three of the plates from which the field was chosen 
and measured seven additional ones. The parallax of 8 Cygni, 
computed with field i, 3, 6, and 9, was found to be ©''.007 ± 
o''.oi9. With the field 2, 6, 7, and 10 the parallax was found to 
be 0^.049 ± o''.oo8. I have not the slightest doubt that the latter 
result is nearer the absolute parallax than the former. Mr. 
Pitman first suggested the desirability of some such method of 
procedure and the method that we actually use was largely 
due to him. 

PART III. 

The Measuring Engine. Methods of Reduction. 

The plates are measured on an engine essentially the same 
in most particulars as that described by Schlesinger in the Astro- 
physical Journal, vol. 33, pp. 10 et seq. The machines are the 
same in the arrangements of the guiding ways; the microscope 
ways; the counter-balancing; the posts carrying the dots for 



l8 JOHN A. MILLER 

rotating the plate through 90 degrees; the manner of comparmg 
the plate with the scale, and of bringing the film always in the 
same plane. They differ in the following respects : The meas- 
uring engine that we use is smaller than the one referred to 
aboA'e, being large enough to receive plates 5 by 7 inches — the 
size we use. The iron plate carrying the photographic plate is 
provided with a circle by means of which position angles may 
be set off. The circle is graduated to degrees, and may, by 
means of a vernier, be read to tenths of a degree. The disk 
carrying the position circle may be clamped to another iron disk 
which rotates about an axis perpendicular to its plane and the 
plane of the plate. This enables the operator to rotate both 
disks through any angle the operator desires. Stops are pro- 
vided rotating them through either 90 degrees or 180 degrees. 
The microscope carries a micrometer the screw of which has a 
pitch such that four turns of the screw correspond to one milli- 
metre (approximately) on the plate. The eye-piece is provided 
with a reversing prism. 

Tlic scale with which the plate is compared is 24 cm. long 
and is graduated to millimetres, but numbered in quarter milli- 
metres. For example, a reading of 400 means that a mark is 
100 mm. from the zero end of the scale. The scale was com- 
pared by the Bureau of Standards with the Standards of the 
United States. The Bureau gave the corrections that must be 
made to any interval in terms of microns at a temperature of 
2 7^° C. All the corrections are positive (that is. each interval is 
longer than its nominal length) ; the corrections are given to 
the nearest half micron, the probable errors of some of the 
corrections being as much as 0.6 micron. Since the scale is 
numbered in quarter millimetres, we multiplied the correction 
given by the observers of the Bureau by four in order to reduce 
the corrections to the same units as the mark on the scale. 
Table I gives the value of each interval from the zero of the 
scale to a given mark plus the four times the correction given 
by the Bureau of Standards. For example, the interval from 
zero to mark numbered 216 is 54 mm. — a correction of 0.0075 
mm. In the table following it is recorded as 216.030. 



DETERMINATION OF PARALLAXES OF FIFTY STARS 19 

Table I. 
96.024 

120.020 260.026 400.036 540.040 680.042 820.050 

124.016 264.028 404.040 544.038 684.042 824.050 

128.018 268.028 408.038 548.038 688.044 828.050 

132.022 272.030 412.040 552.036 692.044 832.050 

136.022 276.024 416.042 556.036 696.044 836.050 

140.020 280.032 420.038 560.036 700.044 840.050 

144.020 284.030 424-034 564-036 704.046 

148.020 288.030 428.040 568.038 708.046 864.052 

152.022 292.028 432.038 572.040 712.046 

156.024 296.030 436.038 576.040 716.044 960.056 

160.022 300.032 440.040 580.042 720.044 

164.018 304-034 444-038 584.040 724-048 

168.020 308.032 448.038 588.040 728.046 

172.024 312.034 452-038 592.040 732.048 

176.024 316.036 456.040 596.040 736.042 

180.024 320.034 460.038 600.040 740.046 

184.026 324-034 464-038 604.042 744-046 

188.028 328.036 468.038 608.044 748.046 

192.028 332.032 472.036 612.040 752-046 

196.030 336.034 476.034 616.044 756.046 

200.024 340.034 480.034 620.040 760.048 

204.030 344-034 484036 624.040 764.048 

208.034 348.032 488.040 628.036 768.048 

212.028 352.032 492.034 632.040 772-050 

216.030 356.034 496.034 636.038 776.052 

220.026 360.030 500.034 640.042 780.050 

224.030 364-030 504-036 644.040 784-050 

228.028 368.032 508.036 648.038 788.054 

232.032 372.032 512.036 652.040 792-052 

236.030 376.034 516.036 656.042 796.052 

240.030 380.034 520.036 660.044 800.052 

244.028 384-034 524-034 664.044 804.052 

248.028 388.032 528.034 668.044 808.052 

252.024 392.036 532.040 672.044 812.050 

256.028 396.038 536.034 676.042 816.050 

The Guiding Way. — In order to test the straightness of the 
guiding way we placed a spider's web stretched approximately 
straight between two plates of glass, which we fastened to- 
gether. These were placed in the measuring engine so that the 
spider's thread was approximately parallel to the guiding way. 



20 JOHN A. MILLER 

\\t measured the distance from the guiding way of various 
points on the thread whose positions were determined by a 
milHmetre scale fastened to the guiding w^ay. The plate was 
then turned through an angle of i8o degrees about the thread 
as an axis, the adjustment being such that each of the points to 
be measured is again opposite the same point on the guiclmg way 
that it was when it w^as first measured. The distance of these 
points from the guiding way was again measured. We then 
found the mean of these two distances for each point of the 
thread from the guiding way. Points at distances from the 
guiding w^ay equal to these means should lie on a straight line. 
The amount of deviation is the error of the guiding way. The 
character of the guiding way was determined by Miss Steele and 
myself in 1914, and again by Mr. Pitman in 191 6. The measures 
were only fairly accordant. But the measures of 19 16 did not 
show that there had been any wear on the guiding way. The 
means of the three measures were as follows : 

Table II. 
Deviation of Guiding Way in Quarter Millimetres. 



Side 


Deviation 


Side 


Deviation 


Side 


Deviation 


scale 


in quarter 


scale 


in quarter 


scale 


in quarter 


reading 


millimetres 


reading 


millimetres 


reading 


millimetres 


90 


+ 0.002 


140 


— 


.005 


190 


+ 0.002 


95 


+ 


II 


45 


— 


2 


95 


5 


100 


+ 


7 


50 


— 


2 


200 


+ 2 


05 


— 


2 


55 


— 


2 


05 


+ 3 


10 


-L- 


5 


60 


— 


2 


10 


+ 7 


15 


— 


I 


65 


— 


2 


15 


- 3 


20 


+ 


I 


70 


— 


7 


20 


+ 5 


25 


_J_ 


5 


75 


— 


7 


25 


+ 2 


30 


— 


I 


80 


— 


2 


30 


— I 


35 


+ 


3 


85 


— 


6 


35 


— I 



The adjustment of the posts for turning the field through 
90 degrees, as well as the determination of the angle between 
the diagonals of the quadrilateral formed by the four posts, was 
determined by Dr. S. G. Barton. He vised the method described 
by Schlesinger. 

The work at the measuring engine is as follows : AA^e have 
measured most of the plates parallel to the ecliptic. At the 
close of the exposure a trail is made on one or more of the plates 
of each series. The telescope is provided with an electric slow 
motion in right ascension which is operated at the e3^e end of the 
telescope by means of a switch. By closing this switch stars 



DETERMIXATIOX OF PARALLAXES OF FIFTY STARS 21 

are made to trail upon the plate. In case the star is too faint to 
trail it is customary to allow the driving clock to drive the tele- 
scope for a short time after it has been displaced by means of the 
switch. We have assumed this trail is parallel to the equator, 
not making corrections for its curvature, which is so small that 
it will not affect the parallax. One of the plates on which is 
the trail is set up and turned through the proper angle so that 
the x-coordinates are parallel to the ecliptic. The other plates 
are set up by making the difference in the x-coordinates between 
any two stars equal the corresponding difference on the first 
plate. The measurement is then as follows : The micrometer 
carries a single wire, and parallel to it a pair of wires set just 
wide enough apart so that if the mark on the scale is placed 
between them a thin strip of silver shows between the mark and 
either of the wires. One can set on a mark in this way with 
great accuracy. The star image is first bisected with the single 
wire with the reversing prism in a given position, then the 
reversing prism is turned through 90 degrees and the star bi- 
sected again. The microscope is then tilted to the scale and 
the double wires set on the mark with the reversing prism in the 
direct and in the reverse position. The microscope is then turned 
to the star, which is bisected again with the reversing prisms 
in both positions. Wq measure the parallax star at the beginning, 
then all the comparison stars, and the parallax star again at the 
end. We always set the double wire on the mark nearest it 
when the microscope is tilted to the scale, so that we never need 
turn the micrometer head through more than two revolutions. 
The part of the micrometer screw used in the measures was 
thoroughly tested by Miss Steele and myself. We selected two 
small dots of about the same size on a plate, separated from 
each other approximately a distance ecjual to one turn of the 
screw, and measured the distance between these points, using 
every part of the screw that is used in the measurements of 
stars. ]\Iiss Steele made three series of measurements and I 
made two series. AA^e concluded that any irregularity in the 
screw was much less than the error of bisection. 

The value of the micrometer screw is determined one or 
more times each day; that is, we determine how much four 
revolutions of the screw differ from one millimetre, and apply 
the necessarv correction to all the measurements. 



•22 JOHN A. MILLER 

The Method of Reduction. 

We reduce our measures by the '' Method of Dependences," 
described and discussed in a most admirable way by Schlesinger.^ 
For that reason much that immediately follows need not be 
written. I have, however, convinced myself of the validity and 
efficiency of the method in the very elementary way, none of 
which is new, discussed in the following pages. I have in the 
end deduced the same equations as Schlesinger did and conserved 
his notation. But I have reached these results in a slightly 
different way. This prefatory remark is by way of apology, and 
the reader need not read it, but may pass over immediately to 
equation (5). 

Suppose we set up a standard plate. Take as origin on the 
scale the zero of the scale and a point just beneath it as the 
origin on the plate, and a line parallel to the ecliptic (or equator) 
which we suppose parallel to the scale as the x-axis. Let this 
axis be marked on the plate in red, and let the coordinates of 
star i {i-i . . . n) referred to this origin and to these 
axes be Xi, yi. 

Let X = — — I y = -^— • 

n n 

These quantities x, y may be set off on the machine, thus de- 
termining a point on the machine which we shall call G\ The 
point immediately beneath it and on the plate we shall call G. 
We may now transfer the origin to G, or to G' (^y~y)- Let the 
coordinates of star i referred to G, and to axes parallel to the 
original ones, be Xi, Yi. 
Then 

Xi = X -\- Xi' 

:. i:xi = nx + i:Xi, 

.•.^Xi = o. 
Similarly S 7^- = o. 

Suppose we take the plate out and later replace it, but that G is 
no longer beneath G', because the plate has been shifted in some 
direction and turned through an angle 0. Let the coordinates 
of G, referred to G' as origin and the measuring and side scales 
as axes, be Xoyo, and the coordinate of star i referred to the same 
axes and origin be x'i, y' i ; then x\ = Xo + Xi cos - Yi, sin 0. 
° Schlesinger : Astrophysical Journal, vol. 2>Z, PP- 161 et scq. 



DETERMINATION OF PAR ALE AXES OF FIFTY STARS 23 

Where x\, y\, Xo, >'o are measured parallel to the scales and have 
G' as origin and Xi, Yi are measured parallel to the red axes and 
from G as origin. Suppose, further, that the relative tempera- 
ture of the machine scale and plate have changed and that the 
change in any length is proportional to that length. Let the 
coordinates of star i, still referred to G and the axes parallel to 
the scale (after plate has been turned), be X\, YU; then, 

X'^ =KXi COS ^ - Z Yi sin + Kxo 
Let K cos 6 = I — a, K s\n = l, Kxo= —c. 
Then 

X'.-Xi + aXi + bYi + c = o (a) 

provided the measures were exact. Since they are not, we write 

X'.-Xi + aXi + bYi + c = Vi (i) 

There will be as many equations as there are comparison stars. 
Equation ( i ) is the same with the same notation as that given by 
Schlesinger and numbered ( i ) ; that is, X^t is measured on the 
turned, displaced, and stretched plate from G' and parallel to 
the scales on the machine. 



Hence, since T^Xi = and 2 Yi = o, 
[X^]a + [X' Y]b = - [XiX' - X)] 
[X- Y]a + [ Y^]b = - [ Y{X' - X] 

n-c= -[X'-X]= -[X'] 

Hence 

^ JYjX' - X)] [X- Y]- [X jX' - X)] [Y^, 
^ [X^ [F2] - [X- F]2 

[X-X'] [Y^]-[X'' Y][X' Y] 



(2) 



[Z2][F2]- [Z- F]2 
[X {X'-X)][X- Y]-[Y(X'- 



X)] [X^ 



[X^][Y^]-[X- F]2 
^ [ X-X'][X'Y]- [X'' Y][X^ 
[X^] [F2j-[Z- F]2 



(3) 



. = - - m. 

From (a) it follows that 

Xi= aX, + bYi + c + X'i (4) 

That is, the x-coordinate of any object referred to G on the 
standard plate and to the axes chosen for the standard plate 
equals the x-coordinate measured on the comparison plate from 
the fixed point on the scale parallel to the turned axes + aX 



24 JOHN A. MILLER 

(measured on the standard plate from G and parallel to the axes 
of the standard plate) + hY, measured in the same way, + c. 

Suppose, instead of setting up the standard plate a second 
time that we set up another plate, and suppose, further, that the 
comparison stars and G are affected in the same way as the 
parallax star is by precession, aberration, and refraction, and 
that they have neither proper motion nor parallax. Let the 
comparison plate be called plate i, and let the two plates be 
superposed so that each of the comparison stars and G are 
exactly superposed. Suppose we mark on the standard plate 
the position of the parallax star on plate i. Call this point 
referred to G and the red axes 

^, ri, then 
X'^= Xn + a'E + hri + c (41) 

If we substitute in (4), 

4" = Xn and t; = Y^ ^ 

and the value of a, h, and c, derived from (3), we get 

m' = X'n +Xn -) 

_ y, j Xi(Z.[P]) - \\{Xn[XY]) + Fi(F.m) - Xx(F4X- Y]) , J_\\ 

"\ [X^][Yn-[XYf ^ n ) >.(5) 

_ ^, f [X,{X.[Y^] - Y,[Xn[XY]) + Y,{Yn[X^) - X,{Yn[X - Y] j^ 
^ n [X^][Y^-]-[XYf "^ 71 

Or, letting D^, 1)2 • • • be the coefficients of -X\, -X\, 
equation (5) becomes 

m' = ^- Xn = X'n - llX'iDi 

In this investigation, these equations, barring the substitutions of 
Ztt, Ftt for ^ and r^, respectively, and the fact that a, h, and c 
have been determined by least square solutions, are true equations, 
not approximations. No terms of any order are neglected. 

The error introduced by the substitution of ^ , '^, for Xtt, Ytt^ 
is smaller than the error of measurement. For example, sup- 
pose the parallax of the star is o''.5, and that the standard plate 
and plate i were taken at the extreme positions in the parallactic 
ellipse — most unfavorable cases — then for an error of orientation 
of 8', of 15', and of 30' the error introduced by the above sub- 
stitution is respectively 0.0005, 0.0009, and 0.0019 revolution of 
the micrometer screw. 



DETERMIXATIOX OF PARALLAXES OF FIFTY STARS 25 

The quantities Xi may as well be measured from any point 
on the machine (e.g., the zero point) as from G', and this we did. 



Fig. 




Let MX be the plate, G' the centre of gravity of the com- 
parison stars, 5 any star whose position projected on x-axis is 
Ai, and let any place on the scale be o. 
Then 

m' = AnG' - ZDA^GK 

= OA^rr - OG^- 5 D {6a~- OG') 
= OAn - OG' -I. DOT, + OG^T, D 
= ~0A^- T,DOAi 

= Xrr - 2 DXi 

where now Xtt and Xi are measured from any point on the scale 
and Di are the quantities defined on page 24. It then becomes 
necessary only to measure the coordinates of the stars, reading 
their positions directly from the scale and by means of equation 
(5) computing the m' for each plate. 

The advantages of this method of reduction are very fully 
and clearly discussed in Schlesinger's paper. The only change 
that we made w^as to compute the D's to four instead of three 
decimal places and round them off to three instead of two decimal 
places. 

We have introduced a correction made necessary by the 
approximate values oi Di. 

According to the form in which we compute D and m, w^here 
D is the absolutely correct value, we should have for our standard 
plate 

m = Xt- y^DiXi = o. 

However, we do not use the absolute value oi D, but compute 
it to four decimal places and get an approximate value. Let us 



26 JOHN A. MILLER 

call this value Da and the approximation De. Then any value of 
Di may be written 

Di = Da 4- De. 

TiDa = I (chosen in this manner) . 

SDr = I (must be, from form of computation). 

In practice we use 



and neglect 



- ZDeXi 



Suppose we could shift the standard plate to the right or left 
without changing the orientation, ^^'e would then have 

m= (X^+O- ZDaiXi + C) - llDeiX' + C) 

= X^+C- ^DaX, - CUDa - ^DeXi - CllDe 
= Xn - llDaXi - UDeXi - CY.De. 

If we again use X- — DaXi, and neglect - ^DeXi as in the 
first instance, we still have to account for the term - c^De, or, in 
other words, the ;;/ in the first case would differ from the ni in 
the second case by this amount. 

It sometimes happens that C is twenty or more quarter milli- 
metres and iDe is not infrequently o.oooi or 0.0002, in which 
case the error might amount to 0.002 or 0.004 quarter milli- 
metres. 

This could be corrected easily by subtracting the X-n- used in 
computing the D's from the mean of the Xtt- on any other plate. 
This gives the quantity C. Then C iDe can be found. 

When jDe = 0.0000. there is no correction. 

Having made this correction, we determine the parallax from 
the well-known equation 

The following table contains a summary of the results for 
fifty stars. The meaning of the columns is sufficiently clear to 
need no further explanation. 



DETERMINATION OF PARALLAXES OF FIFTY STARS 27 



to W K) K) to 
Cn 4i. 00 K) NH 


g^ 




00-^ OS 


ol^ c!n 


to HH ^ 00"M ON 


ai4^0J to HH 


2 

c 




+ 1 








+ 


1 




+ 


W 


CsO-> Cn -P^ K) 


4i. HH 




|_4 


i-( 


to to 


to 1-H to to 


OJ 4^^ Cn to cn 


O 


HH C^ CN ^'O 


10 to 




00 to to 


oi « 


^ \o to to 


^ ON^ 00^ 

o 


s 
cr 


w K> w KJ « 

to N- -p>. oc 


« to 

vO 4^ 




00^ 00 


•<I 01 ON 


-^ " .??,*? r^ r^ 


ONCn HH w 00 


4^ 4i» Oi ^J 00 


ai4^ 




ONCn Cn 


00 to 00 


CfN ON^C^l Cji OJ 


Cn OJ Cn O 0^ 


(7\-<i vO 0^ 


ONVO 




-av0 4^ 


\0 00'^ 


to 4i^ 004^^ NO ^ 


Cn ON O C/J Cn 


or^^wr 




^ 


^ 


"Cfc « 


hdr^' 


zr o-^r^o 


to jvj-^ "> t-J 




to P dn^P 


9^9%7i 


3 ^Oto 

P fD - 


< p ,. op p 


2. I'g 




oj 3 q'Sis 


-Ta 3 


3 


3 3 


►H p 


^ 3 q HH 


P 3 t 


r 2. 3 c: -C- 




oi C. w c ci. 


^ ^?5 








3 


f-^a. ;t; ai^ .i^* 




ra 8 "-^ 


P2 3 




3 2 




3 O! 3 -H 




^ 3 rD ^ ^U 




<-i p c^ to 
00*— '-OJ 00 


^•0 


f 


p" 


1 
3 


w to 

4^^ 3 


5 ^ 


2 fT) 

p' f-^ 

F9 


op 


en CN 


§.^ 


p^ 


W 

m 





vO 


4^ 






w' 


Cfl 










3 
































3 


3 






p 








„ M 
















;s- 


r^ 


NH VO 






00 




^ 




3NCn 4^^ 


to ©5^ 


> 


K) Cn to M >-< 


Cn HH 






Cn 01 


C/J cn 


^ 4^^ Oi OJ 4^ OJ OJ 


4^ 4^ OJ a 
^ ^ OJ OJ 1-1 S. 




p-<r 4^. ON K) 


-f^ V" 




ON 


oo-<t 


4^ -p. 00 


vO Cn 


D |H Cn ON ON 


o 


•<i vb to 6j b 


to -M 




in 


00 « 


« to w 


OJ -^ 


O -ji' "^ "to to 


4^ On b OJ b ? 


§ 




+ 1 










+ 1 


+ 


+ 




ONO0Cn4^ K) 


4^ HH 




1— 1 


l-l 


to to 


Oj 


(0 I-H to to 


OJ 4^^ Cn to Cn 


HH OV NHVO 


to to 




^ 


to to 


cn NH 


to ^ NO to to 


■vi ^^ 00^ 


Oi c^ Ca) -p- 


1-. I-H 




Cyi 


<i^ Cn> 


to to 4^ 


« to 


fO HH Oi 4:^ 4:^ 


Cn -H ^ Cn 


^s' 


00 00 o-P' 


HH 00 




^ 


cn ON 


^ Oi to 


Cn C/i 


to Ol 4^ ON ON 


On i-i ^J (O^OJ 


§• 


Cn -vi^ Cn -^ 


4^ ON 




ON 


00 4^^ 


p f^^, 


< Cn 


av4i. ^ 4i. ^ 


Cn ONOJ 4^ ON 


c.^ 


if\ 00 00^ 


J- b 




b 


■M Cn 


OiCn i; 


E^ 00 NO -fi' vb OJ bo 


ON b ONCn HH 


C &5 
















OJ 


OJ 4^ to 


«i 3 


^ ^Q 


^^ 




^ 


W 


:^:^o 


P 


W: >: 


t^^hrjQ^ 


3? 


1 + 


1 






+ 


1 




+ 1 


0+ 1 




b b b b 


b b 




b 


b b 


b b'o 


b 


b • ho 


b ':\'^bb 


!? 


04^ to « 


U> HH 










^ HH 





o 


o o 


o r^oj h; OJ 


o 


ON l-l ^ 


00 ^o 




4^ 


01 to 


On to OJ 


Q 


ON 


O HH 


4^ "^NO -M to 


•d 


Oi Oi ^ OJ 


00 « 




Cs 


Oj on 


CTn - • 


Ol 


to 


ft 5r 


^ ^.O OJ \o 

-• 3 

1 1 


^ 










1 + 








1 


3 

o 



















P. to ? 


^. 


p -f^ . 










i-i 






. -^ to . , ' :; 


o 

3 


b "~J b " Cn 


tovb 




H 


« b 


b 4^ b 


|_( 


OJ b b 


O "-^ Cn to O 




^ 4^ C^ Oi i-. 


ONVO 




1— 1 


« ^o 


Oj 00 


^j 


O to-^ 


00 * o to -P^ OJ 




vo ON 00 to 









00 vC 


to 00 


cn 


^ to to 


to OJ to 00 00 














+ 


1 


+ 1 


+ 




b-i^ « b b 


b b b 




b 


b b 


to b b 


b b 


o b b b b 


b b '<-< b b 
to ON oono Oj 


nS 


Cn 4^ 00^ 


00^ OJ 




OJ 


OOCaJ 


00 HH P-H 




Fi- to O M Cn 


«OJ Cni CX3 


ONOi C/1 







to Cn 


^ SO ^ 


NO cH 


00^ OJ to OJ 


Cn NO to On O 

H- 


■-1 


b b b b b 


b b b 







2 2 


bob 


^ 2 


2 8 2 *2 ^ 


. P. . ^-^ 

b b b b o 


X 




M I-* 












w 








CfJ to ^Oi 


Cn ^ i-i 




^ 


-o 00 


to ^ 


OJ 00 c 


^ ON4i' OJ nD 


HH so NO Cn 00 




>-l l-< ►H to l-H 







^ 




H. « HH 








w ^ 

^p 

^o 


to 4^ to to 


to to 00 




OJ 


to -^ 


M to to 


4^4^- 


i-i to o to to 


to to 4^ to to 


^^rr^^r 


r tr^ 




r 


r t:^ 


t-^r r 


rr 


r r rrr 


t-' f t-" f r' 




• 













000 





o o o o 


o o o o o 


►. o 


K. 3 3 3 3 

f^Crq crq OQ CTQ 


:=s 3 




3 


3 p 


333 


3 ts 


3 3 3 3a 


3 3 3 3 3 


3 O 


crq crq 




OfQ 


crq crq 


OQ Grq crq 


crq crq 


X) crq 


'q crq crq 


crq crq oq c/q crq 



28 



JOHN A. MILLER 



MM &jO tuO^ M bJOMtxCMtuO bjOMbjOfcjOM tuObjObJObjOWifcjO M &jO<: W) bX) 

CC CC^C CCCCC CCCCC CCCCCC GC^CC 

OO OOrO OOOOO OOOOO OOOOOO OOrOO 

^hJ JJP:^^ h:] kJ kJ K-^ h4 JhJJk:!^ Jk:!,^^J!Jj hJ h:i fi^ h^l hJ 

HHM MHHI-II-I |_(l-ll-ll-ll-( OJMMi-HHH MMMI-HMM |_|_lh-lt-<hH 

HHHH oOi-ihi wOOOO mOi-hOO i-(00(NhhO wOi-iCO 

CO q q q q q q q q q q q q q q q q q q q q q q q q q 

4^ 

\00 H-irOOOrO ^mvoO'"' Qi-i^ONf^ O0l-lC^^^!^0 c^OOi-ii-i 

hii-H i-iM(NrO iOfOX)OS? OOOOC^^i-i i-iOCONClt^ ^Cr<iCNoOC 

wO OOOO OOOOO OmhhO'O OCrC(NOO OOOhhi-h 



O c3 



o 
+ I 



I + 



+ 



+ ^. 



I + 






01 VO 

ro O 

o o 



+ 



O O CO O 



01 lo 'i- ^r:: 

01 r^\o '-' 

M O ro O 

O O O o 



O o) o r^ 
O O O CO 

lO l-H HH O 



O ON w o 

lOVO CO ID 

(^ HH - O 

OOOO 



t^ oi r^ oi 

rO -xl- 01 O 
O O) rt- O 



00 rt- O O 
HH ^ ONOO 

O O Ol ON 



I + 



'xh fO re '^ 

r^ 01 r^ Ol 

o lo M o 

O rO O O 



'^ 

01 t:|- 
01 lO 

o o 



01 01 
Ol Ol 

01 O 



+ 



kB 



<< < 



Ph \4<0 m PhMO< P^feM PhP^" fe<c5MO 






01 lO 

oi lo 






\0 CO rOOO > 



CO i-H 01 q 01 

lO '^ lO ro CTn 



r^tso GOO ooivot^ON 



c ^r;^ 



00 1-, 



00 



i-irOrO cOOl OliOt^iOOl 



.§4 4 



00* M O* 

H-l ^01 



l^O lO O VO O '^ ro ONOO 



ON lO "^ 00 



tJ- rO r^ lOOO 



01 tuO 
Ol'C 

O C ro g 

(U CTJ 00 O , 

CQ.)-4P<I CQ.O 3. 



I 00 o 
1 OI O 



o s o 2 ^ 



i5 Co 



•;=: 00 



ro 



o a ^ 

oir^ 

01 I^CQ'<: 



'5 Bv !^ >. S rt 



o 

^ c. t:: PQ 00 



M 







l-H vO 


t^ Ol 


'd-'^'d-l 


00 


01 r^-d-oi 


ONr^f CO 


O CO 


rO H- ^ O '^ 


00 00 00 


to rO 


CO 01 00 01 o 
\0 r^oo vO 00 


t^OO >0 CO '^ 


\0 CO '^ 


'd-O 


CO ^ O NO CO 




rOiOOO 


lOO 


^ 


Tt- 01 01 01 


CO 01 CO 


01 ^ 


lO t^ O ONf^ 


^ 


01 01 01 


01 0< 


Ol Ol 


01 Ol 01 


HH 


CO CO CO CO 


'^ ^ ^ 


^^ 


"^ 01 HH 01 "^ . 




lO HH ON 


Ol r^ 


r--.vo 


hH 00 CO 


„ 


01 01 Th tj- 


TfuOOO 


t^ -^ 


^vO ^M3 NO 


d 




'^ rO 


CO 01 


CO 01 CO 


vO 


CO "^ -^ 


HI ro CO 


' CO 01 


01 lO t^ lO 01 


pq 


+ 


















6 


vo r>.oo 


OnO 


i-i 01 


CO Td-lOl 


vO 


t^OO On O 


HI 01 CO 


-^lO 


NO r^oo ON O 


^ 


01 M N 


0< CO 


CO CO CO CO CO 


CO CO CO CO -^ 


■rt- -^ ■Tj- 


'=j- -xh 


'^ '^'^'vf-iO 



DETERMIXATIOX OF PARALLAXES OF FIFTY STARS 29 

\\'e are emphasizing at this observatory the determination 
of the parallax of binary stars whose orbits are well determined. 
From the preceding table have been selected all such binaries 
whose parallaxes are positive. Choosing for each binary those 
elements of its orbit that seem best, we computed the linear 
dimensions of the orbit, the mass and the Ituninositv of the 
system in terms of the mass and luminosity of the sun. The 
table which follows exhibits the results. A\'e have also found 
the ratio of the mass to the luminosity and written it in the 
column headed y' The last column contains the name of the 
computer of the elements of the orbit that we have used. 

The most significant facts shown by the table are that in 
general the sizes of the orbits are of the same order of magnitude 
as those of the outer planets ; that the masses and luminosity 
of the systems are comparable with those of the sun. Practically 
all the spectra belong to the types F and G. We had rather ex- 
pected that the ratio ^ would run more nearly uniform than 
it does. 



30 



JOHN A. MILLER 



> 


1 


-H-T^' • • 




A 




^ r^* 


-^ . . . E 




^ 


^ ^ c C 




^ 


c 


c ti ^ 


;i C C C rt 


+J 


o S 1^ "y 




<u 


OJ 


(D S <D 


(D QJ a-i a; ^ 


3^ ^ 


^ 


^^^^ 




Si 


..-^ 


^X2 .X2 


^^^^ c 


^ :3 


o 


QQ<< 




a 




^ala 








00 m H-. c^j 




i^ 


vO <N 


HH 04 CO CO 


10 ON rf 10 


CO 


J IS 


00 10 (N Th 




00 


UO^ 


rj- 10 « ^ 


m3 ^q 01 i^^q 




d «■ 10 6 




d 


d t^ 


10 10 '^ lO 


d COOO ^ t-^ 


i_I 




00 








<N 






C >>M 


rO t^ m t^ 





CN 


irjvO 


00 vO CI 


r^ uo 


VO 


'S-- " 


1000 i-i 


r^ 


10 


01 00 


^-I^O 4 


01 as^ q 


t^ 


^SO 


ub «■ h; d 


X 


CO 


d rO 


00 HH CO i-i 


i-J d CO d CO 


d 


l-H O) 










HH t^ 




W M 


10 -i t:|-vO 




10 


10 (N 


CO M r^ 


HH UO '^ 


t^ 


rt II 


(S (N 11 10 







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10 (N vo r^ 


qv 01 10 ^ 





SO 


\d « d 00 




'd- 


d d 


H;_d H.; c^ 


H^ d ^ 10 d 


d 






rt- fO to 




vO 


fO 


^ ON -xl- ON 


01 ONO 01 


^=4- 


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t^ 


H-i t^ ro r^ 




'^ 


ON 


^ "^ "^00 


CO HH 00 10 r^ 


r>. 


.0 




1-1 d 10 ro 




^ 


06 r^ 


tI-h^ d 4 


Tj-oo 01 01 CO 


r^ 


•^10 (N 




M 


'-' 


HH (N (N h- 


01 01 CO 












OJ 


<^ ^ 


i^ 




c? 









vO 


ON 


t--0 10 


01 




S 


< 


^00 \D c^ 




10 


00 


vO ^ CO 10 


01 TtOO HH ON 


01 


'1" 'I" '^ '1 




00 


vq t-. 


04 (N r^ CO 


10 q Td- ON 01 


00 


CO 




%H OSO 










HH « 


^« 







i/^ t^ rO i-i 




CO 


ON 


04 0) CO 


>vO ic ON r^ 




'd 


»O00 fO^_ 




°S 


CO ^ q 10 


\q 00 t^ q CO 


CO 


■n 


>^' t^ co^* 




q 


^--^ 


ri- d\ CO ^ 


^ LOO t>- '-I 


M3 


<u 


to (N, fO HH 




d 


CO t^ 


•^^ HH t>. ro 


00 Tf O) '^ ll 


01 


(1. 


C CO 









01 








9 9 9 9 


t^ 


„ 


10 CO 10 


t-» HH vc r^ 


g^ ON « j^gN 


00 







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« « 


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q 


q 


9 9 9 


9 9 9 9 


q q q q q 


9 


X 


"d 














rt 


4i 














rt 


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10 


00 i-i i-i 


CO ^ « 


1-* 01 CO CO 


^ 


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ro 


rO 


t^ 10 « 


i-c VO cOOO 


00 01 ^ O) t^ 





CL, 


q ^ q 
+ 


q 


q 


9 9 9 


9 9 9 9 


HH „ q q q 






fofefe 




fe 


fe< 


M<0 


t^Ofefcfe 





■5 <1> 


Ti- 






t^ "-H 


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t^ HH d CO 


to 


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w vq vq On 


vq 


CO 


"9 "t " 


vq vq q\ q 


q 04 t^oo q 


00 


vO rO »0 t^ 


IC 


^ 


r^ lib 10 


vd vd CO CO 


^uo CO CO 10 


10 




V; r^o ^ 




t^ 


C 00 T:t- 


^ r^ r-- 


>- t^ iTj r^ HH 


^ 


§ 


10 hH 10 10 




10 


COIO 


r^j- ro '^ 


CO rf- " CO HH 


CO 


0\ 




r>. i^ t^ 




r^ 


ON « 00 


t^^o - 


01 01 ':t-r^ 10 


v£) 


^ 


10 10 ro i-i 

+ 






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ro Oi CO 


CO 1^ CO 01 


01 





• HH ro t^ 10 







(N 00 


00 J^ 


CO 01 


^ 


•S '^ "^ Tf 






i-i CN ^ 


01 CO CO 


10 CO HH ^ 


10 


o» 


§ 














M 


V 0) '^ 




00 


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10 


00 « 


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ti 


-« 










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01 




«if 




6 

f 






g_ 1 

a HH M 

•>5 P ^ 

CO S O; 






u 


II o< 1; 1 




6 


» 1 
If 


00 
■^ 00 








cj 






10 

00 


^' 


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10 



DETERMINATION OF PARALLAXES OF FIFTY STARS 31 

PART IV. 

Obserz'ational Data, Solutions, and Result. 

In the detailed results that folloAv there is given for each star 
its BD number, together with some other ordinarih^ used desig- 
nations ; its position given to minutes for the epoch of 1900; its 
magnitude, taken, if possible, from Harvard Photometry; its 
proper motion, taken, if possible, from Boss's Fundamental Cata- 
logue ; its spectrum, taken from the Annals of Harvard College 
Observatory, vol. 50. 

The observational data for each star are given in Table i. 
Columns i, 2, 3, 5, and 7 need no explanation. The initials in 
column 4 have the following signification: B. denotes Barton; 
Ma., Matos; M., Miller; P., Pitman; S., Miss Steele. It is our 
custom to examine under the microscope all plates soon after 
they are developed. At that time the quality of the images is 
estimated. There are five grades that we measure — i, 2, 3, 4, 
and 5 : the higher the grading, the better the plate. The quality 
of the image in column 6 is usually that assigned at this exam- 
ination. It is occasionally changed by the person who measures 
the plate. 

For Table 2, which contains the data that enter into the 
reduction, only columns 2 and 3 need comment. In column 2 is 
given the weight of the plate assigned by the person who measures 
it, the quality of the images and the number of exposures being 
the chief elements entering into the weight. T is the time of 
the observation given in days from the mean epoch of the series. 

A table, not numbered, contains the data of the comparison 
stars. The coordinates X and Y are referred to the parallax 
star as origin, and are measured in the coordinates in which 
the parallax star is. They are given in quarter millimetres. The 
normal equations follow, together with their solution. The 
proper motion, /x, is given in seconds of arc per hundred days. 

B.D. + 57°2865. 23062. (o^^i'-.o, + 57° 53'-) 
Mag. 6.1. // = -h 0^6329; +o".038. Spectrum F. 

The measures were made in longitude. The star is a close 
binary with a period of 105.55 years. After some experimenta- 
tion the exposures were made long enough so that the images 
of the components could not be separated. The resulting image 
of the parallax star was long. We bisected this long image. 

Russell finds for this star a hypothetical parallax of o".046. 



32 



JOHN A. MILLER 



Table i. 



No. 


Date 


Hour 
angle 


Observer 


Xo. of 
expo- 
siires 


Quality of 
images 


Xo. of 
inter- 
polations 


I 
2 


Dec. 9, 1912 
Dec. 12, 1912 


hr. nun. 

+0 15 

00 


M. 
M. 


3 

2 


3 
I 


I 
I 


3 


Nov. 20, 19 14 


-0 30 


P. 


3 


4 





4 
5 
6 

7 
8 

9 


July 22, 1915 
July 24, 19 1 5 
Aug. 14, 1915 
Aug. 15, 1915 
Aug. 17, 1915 
Aug. 18, 1915 


-0 33 
10 
26 
53 

55 

1 


P. 

AI. 

P. 

P. 

P. 


3 
3 
3 
3 
2 

3 


4 
4 
4 
4 
3 
3 












10 

II 

12 


Dec. 22, 1915 
Dec. 26, 1915 
Dec. 31, 1915 


-0 6 

+ 20 

17 


P. 

AI. 

P. 


3 
3 
2 


3 

^3 


I 
I 

1 



Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(V) 


by 


I 


.8 


-8.24 


-0.694 


— O.I4I 


.007 


AI. 


2 


.6 


8.21 


-732 


.122 


.012 


AI. 


3 


•9 


-I-I3 


— 0.420 


-0.044 


.003 


AI. 


4 


-9 


+ I.3I 


+ I.OI4 


+ 0.005 


•005 


AI. 


5 


.9 


1-33 


I.OI5 


— O.OOI 


.001 


AI. 


6 


•9 


1.54 


0.958 


+0.006 


.003 


AI. 


7 


.9 


1-55 


.952 


— 0.002 


.005 


AI. 


8 


.7 


1-57 


-939 


+ 0.002 


.001 


AI. 


9 


•9 


1-58 


.933 


0.006 


.003 


AI. 


10 


.8 


+2.84 


— 0.829 


+ 0.021 


.012 


AI. 


II 


.8 


2.88 


.864 


.003 


.006 


AI. 


12 


•7 


2-93 


.902 


.005 


.004 


AI. 







COMPARISON 


STARS. 






No. 


X 


F 


Depend- 
ence 


Diameter 


B. D. No. 


Mag- 
nitude 


2 

3 

5 

9 

10 

TT 


-129.542 
+ 198.941 
2.075 
9.183 
- 80.656 
+ 46-503 


+ 138.754 
-165-757 

240.594 
+ 100.661 

166.938 
29.588 


+ O.III 

0.383 

-0.035 

+0.316 

0.225 


0.50 
0.36 
0.38 
0.44 
0.42 
0.52 


+57° 2858 
2867 

2866 


8.8 
9.2 

9.1 



Normal equations 



Solution; 



9.800C+ 1.770M+ i.6867r= —0.190. 

+ 126.413 +10.309 =+i.66i, 

+ 7.477 =+0.142. 

06l=to".002. 



p. e. unit weight ='=o".020. 



M=+0' 

c = — o .023. 

7r= +0".030 



= o".oo8, 



DETERMIXATIOX OF PARALLAXES OF FIFTY STARS 33 



B.D. + 28°i03. f Andromedae. (o^33°^.3, + 28°46'.) 
^lag. 4.52. u = -0^0174; — o".248. Spectrum G5. 

The measures were made in longitude. 
Slocum found a parallax of this star of o''.042 ± o''.oi4. 

Table i. 



No. 



Date 



Hour 
angle 



Observer 



Xo.of Xo. of 

expo- Quality of inter- 

sures images ; polations 



hr. ynin. 



I 


Dec. 


12. 


1913 


+ 


30 


P. 


2 


Dec. 


13, 


1913 


I 





M 


3 


Dec. 


30, 


1913 





5 


P. 


4 


Jan. 


6, 


1914 





38 


P. 


5 


.July 


29, 


1914 


— 


5 


S. 


6 


Aug. 


23. 


1914 


+0 





P. 


7 


Sept. 


4. 


1914 





50 


P. 


8 


Dec. 


12, 


1914 


— 


16 


M 


9 


Jan. 


I, 


1915 


+0 


24 


P. 


10 


July 


22, 


1915 


— 


26 


P. 


II 


Aug. 


14, 


1915 


+0 





P. 


12 


Aug. 


15. 


19 1 5 


— 


6 


P. 



Table 2. 



No. 



Weight 

of plate 

(P) 



Time in 

100 days 

(T) 



Parallax 

factor 

(P) 



Solution 
(m) 



Residual Measured 
(V) by 



I 


-/ 


-2.79 


-0.858 — 


179 


.015 


s. 


2 


.8 


2.78 


.867 


161 


-003 


s 


3 


i 


2.61 


•965 


162 


.008 


S 


4 


.8 


2-54 


.981 


157 


.014 


S 


5 


I.O 


0.50 


+0.972 1 


187 


.012 


S 


6 


I.O 


0.25 


-765 


177 


.008 


S 


7 


.8 


0.13 


.614 


191 


.001 


S 


8 


.8 


+0.86 


-0.857 i 


253 


.010 


S 


9 


.8 


1.06 


.970 


253 


.004 


S 


10 


.9 


3.08 


+ I.00I 


260 


.009 


S 


II 


I.O 


3.31 


.860 


256 


.003 


s 


12 


•9 


3-02 


.851 


249 


.0X2 


s 







COMPARISON 


STARS. 






Xo. 


X 


; Depend- 
Y ence 


Diameter 


B. D. Xo. 


Mag- 
nitude 


2 

3 

I 

IT 


+ 132.441 
-244.844 

66.033 
+ 178.436 
- 56.879 


+ 13-767 +0.146 

- 59-207 1 .569 
+ 87.211 —0.051 

- 41-770 +0.336 
50.153 


0.28 
0.72 
0.65 
0.19 
i 0.96 


+28° 105 
100 
104 

106 


9-4 
9-4 
9-3 
9-0 



Xormal equations: 

10.300C+ I.455M+ 0.441-= -2.145. 
+53-473 +13-626 =-1.175. 
+ 8.09S = —0.219. 
Solution: At = — o".ioi =o".oo6. 

c= —o .206. 
- = +0". 096=0". 015. 
p. e. unit weight —0^.031. 



34 



JOHN A. MILLER 



B.D. + 57°i50. ?/Cass. = S6o. (oh43'^.o, + 57° 17'.) 
Mag. 3.64. /^ + oM39o; — o".522. Spectrum Fg. 

The measures are in longitude. This is a binary star with a 
period of ^^7.^7 years. 

Other parallaxes published are as follows: By Russell, o^'.iSq 
(photographic). By Peters (heliometer), o''.i8. By Davis 
(photographic), 0^.443. By Russell (h3^pothetical), o".i6o. 

Table i". 











No. of 




No. of 






Hour 




expo- 


Quality of 


inter- 


No. 


Date 


angle 


Observer 


sures 


images 


polations 






hr. min. 










I 


Nov. 28, 19 1 2 


+ 


M. 


3 


3 





2 


Nov. 29, 1912 





B. 


3 


3 





3 


Nov. 30, 1912 


— I 12 


S. 


3 


4 


I 


4 


Dec. 13, 1912 


+ 


B. 


3 


4 





5 


Dec. 15, 1912 





S. 


3 


4 





6 


Aug. 15, 1915 


-0 13 


P. 


1 3 


4 





7 


Aug. 17, 1915 


I 6 


P. 


3 


4 





8 


Aug. 18, 1915 


I 12 


P. 


i 3 


2 


2 


9 


Aug. 22, 1915 


14 


P. 


3 


5 





10 


Aug. 23, 1915 


I 


P. 


i 3 


4 





II 


Aug. 25, 1915 


I 


P. 


': 3 


4 





12 


Dec. 12, 1915 


-0 13 


s. 


1 3 


5 





13 


Dec. 15, 1915 


13 


p. 


! 3 


3 





14 


Dec. 22, 1915 


16 


p. 


1 3 


4 






Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(V) 


by 


I 


I.O 


-6.67 


-0.452 


-0.561 


.001 


S. 


2 


I.O 


6.66 


.470 


•564 


•005 


s. 


3 


.8 


6.55 


.482 


•575 


.015 


s. 


4 


I.O 


6.52 


.668 


•559 


.001 


s. 


5 


I.O 


6.50 


.692 


•555 


•005 


s. 


6 


•9 


+3-23 


+0.984 


.018 


.004 


s. 


7 


.8 


3-25 


•975 


.026 


•013 


s. 


8 


.8 


3.26 


.971 


.017 


.004 


s. 


9 


.8 


3-30 


.948 


.004 


.008 


s. 


10 


•9 


3.31 


•943 


.013 


.002 


s. 


II 


•9 


3-33 


•930 


.010 


.001 


s. 


12 


.9 


+4.42 


-0.645 


•015 


.003 


s. 


13 


•9 


4-45 


.684 


.025 


.006 


s. 


14 


•9 


4.52 


.765 


•023 


•005 


s. 



DETERMINATION OF PARALLAXES OF FIFTY STARS 35 



COMPARISON STARS. 









Depend- 






Mag- 


No. 


A' 


Y 


ence 


Diameter 


B. D. No. 


nitude 


3 


-167.512 


+ 151-214 


+0.199 


0.60 


56° 128 


8.5 


4 


+ 42.181 


27.484 


0.261 


0.39 


57° 155 


9.4 


6 


166.439 


6.749 


0.295 


0.37 






13 


— 41.IIO 


-185.448 


0.245 


0.77 


57° 145 


8.9 


X 


+ 16.689 


6.063 




0.42 







Normal equations : 



Solution 



12. 600c— 2.888m+ o.3337r=— 2.832. 

+317-669 +25.170 =+17.305. 

+ 7.544 =+ 1.466. 



p. e. unit weight ±0". 022. 



Ai= +0". 232=1=0". 001. 

c = — o .212. 

n- = +0". 1 82 =t= o".009. 



B. D. +46° 536. 2 228. (2^7- 6, +47° I'.) 
Mag. 6.03. // = o". 112 in225°.3. SpectrumF. 

The measures were in longitude. This star is a binary, the 
orbit of which is very uncertain. 

Russell finds a hypothetical parallax for it of o" .026. 

Table i. 













No. of 




No. of 








Hour 




expo- 


Quality of 


inter- 


No. 




Date 


angle 


Observer 


sures 


images 


polations 








hr. min. 










I 


Dec. 


II, I9I3 


— 07 


M. 


3 


2 


I 


2 


Dec. 


19. I9I3 


20 


S. 


3 


4 





3 


Dec. 


29, I9I3 


+0 10 


P. 


3 


4 


I 


4 


Jan. 


I, I9I5 


+0 18 


P. 


3 


2 





5 


Jan. 


15. I9I5 


-0 12 


P. 


2 


I 





6 


Aug. 


14, I9I5 


-0 5 


P. 


2 


5 





7 


Aug. 


15, I9I5 


32 


P. 


2 


3 





8 


Aug. 


17, I9I5 


22, 


P. 


3 


2 





9 


Aug. 


18, I9I5 


21 


P. 


3 


3 





10 


Aug. 


22, I915 


15 


P. 


3 


5 





II 


Aug. 


25. I9I5 


18 


P. 


3 


3 





12 


Jan. 


7, 1916 


+ 


S. 


I 


3 






36 



JOHN A. MILLER 



Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(V) 


by 


I 


.8 


-4-39 


-0.523 


-0.013 


.002 


S. 


2 


-7 


4-31 


.635 


-025 


.009 


S. 


3 


•9 


4.21 


-757 


.Oil 


.008 


S. 


4 


•7 


-0.53 


-.787 


-063 


.Oil 


S. 


5 


-7 


-39 


.909 


-054 


.001 


S. 


6 


•9 


+ 1.72 


+ 1.010 


•044 


.001 


S. 


7 


.8 


1.73 


1.008 


-055 


.005 


S. 


8 


.8 


1-75 


1.004 


-045 


.000 


S. 


9 


-9 


1.76 


1.002 


.046 


.001 


s. 


10 


I.O 


1.80 


0.989 


.049 


-003 


s. 


II 


.8 


1.83 


-978 


.040 


.007 


s. 


12 


.6 


+3-18 


-.844 


.081 


.004 


s. 



COMPARISON STARS. 



No. 


X 


Y 


Depend- 
ence 


Diameter 


B. D. No. 


Mag- 
nitude 


2 

4 

7 

II 

TT 


+ 143.599 
181.555 

-156.249 
168.906 

+ 2.977 


- 59-678 

+ 143-520 

III.517 

-195-358 

73-572 


+0.375 
0.154 
0.061 
0.410 


0.37 
0.58 
0.32 
0.29 
0.42 


+46° 541 

46° 535 


9.3 
9.5 



Normal equations: 



Solution 



9.600C+ 0.126^1+ i.9547r= —0.406. 

+66.957 +14-714 =-0.374. 

+ 7.640 = —0.104. 



p. e. unit weight ±o".oi8 



M = — o".04i ±o".oo3. 
c = -o .045. 
+ = +o".o69±o".oo9. 



B. D. -h 37° 655. 20 Persei = ^524. {2^7^^, + 37° 56'.) 
Mag. 5.6 — 6.7. ^ = + 0^0047; — o".o82. Spectrum F. 

The measures were in longitude. This star is a binary with 
a period of 33 years. 

Slocum and Mitchell found (photographically) for this star 
a parallax of -o".oi2. Russell finds a hypothetical parallax of 
+ o".oio. 



DETERMINATION OF PARALLAXES OF FIFTY STARS 2>7 



Table 











No. of 




No. of 






Hour 




expo- 


Quality of 


inter- 


No. 


Date 


angle 


Observer 


sures 


images 


polations 






hr. mill. 










I 


Dec. 29, 1913 


+0 7 


P. 


3 


5 





2 


Jan. I, 1914 


— 26 


P. 


3 


5 


I 


3 


Jan. 5, 1914 


10 


P- 


3 


5 





4 


Sept. 21, 1914 


14 


P. 


3 


5 


I 


5 


Sept. 22, 1914 


7 


P. 


3 


4 





6 


Sept. 28, 1914 


20 


P. 


2 


3 





7 


Sept. 30, 1914 


+0 27 


M. 


3 


4 


I 


8 


Oct. I, 1914 





P. 


3 


5 


I 


9 


Oct. 2, 1914 


-0 17 


P. 


3 


5 





10 


Dec. 18, 1914 


+0 10 


P. 


2 


2 





II 


Jan. 4, 1915 


— 10 


P. 


3 


5 





12 


Jan. 10, 1915 


+0 


P. 


3 


4 


I 



Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(V) 


by 


I 


.7 


-2.29 


-0.713 


+0.054 


.009 


S. 


2 


.8 


2.26 


.748 


.072 


.009 


S. 


3 


.8 


2.22 


.791 


.063 


.000 


M. 


4 


.8 


+ 0.37 


+0.800 


.086 


.010 


M. 


5 


•9 


0.38 


.789 


.070 


.006 


H. 


6 


.6 


0.44 


.720 


•075 


.001 


M. 


7 


.7 


0.46 


.695 


•075 


.001 


M. 


8 


.7 


0.47 


.683 


.063 


•013 


M. 


9 


.7 


0.48 


.670 


.085 


.009 


M. 


10 


.8 


+ 1.25 


-0.565 


.076 


.006 


M. 


II 


.6 


1.42 


.778 


.069 


.000 


M. 


12 


.6 


1.48 


.838 


.065 


.005 


M. 



COMPARISON STARS. 









Depend- 






Mag- 


No. 


X 


Y 


ence 


Diameter 


B. D. No. 


nitude 


I 


-240.025 


+ 134497 


+0,261 


0.39 


+37° 651 


9-3 


2 


96,920 


— 172,402 


0,195 


0,44 


37° 652 


8.7 


3 


+ 99.313 


+ 157,480 


0.301 


0.33 


37 658 


9-3 


7 


237.630 


-119,576 


0.243 


0.37 






IT 


6.147 


+ 19-837 




0.37 







Normal equations : 

8.700c 



Solution : 



p. e. unit weight ito",023. 



- o,558ju+o,o647r = o.62i. 

16.293 +3-297 =0.006. 

+4.706 =0,035. 

/JL = +0". 008 ±0". 006. 
c = +o .071. 

7r = +0".025±0".0II. 



38 



JOHN A. MILLER 



B.D. + 22° 737. o2(App.)54- (4M6-.2,+ 22° 46'.) 
Alag. 7. 8. ,« = — o^ooI6; — o".042. 

The measures were in longitude. This star was on the same 
plate as t Tauri (see next star). The parallax was reduced, 
using four comparison stars. Two of them, number i and 
number 6, were also used in reducing the parallax of -r Tauri. 
The same set of plates were used to determine the parallax of 
this star and r Tauri, and the measures of all the comparison 
stars of both fields were made without removing the plate from 
the machine. No other parallax of this star has been published. 

Table i. 













No. of 




Xo. of 








Hour 




expo- 


Quality of 


inter- 


No. 




Date 


angle 


Observer 


sures 


images 


polations 








hr. min. 










I 


an. 


I, I915 


+0 07 


P. 


2 


2 





2 


.an. 


5. 1915 


46 


M. 


3 


3 


I 


3 


Feb. 


10, 1915 


14 


P. 


3 


5 





4 


Oct. 


3, 1915 


-0 45 


P- 


3 


4 





5 


Oct. 


12, 1915 


15 


P. 


3 


4 





6 


Oct. 


23, 1915 


+0 40 


S. 


3 


2 





7 


Oct. 


24, 1915 


50 


P. 


3 


3 





8 


Oct. 


30, 1915 


5 


P. 


2 


3 





9 


Jan. 


23, 1916 


+0 20 


s. 


2 


3 





10 


Feb. 


19, 1916 


I 15 


Ma. 


2 


2 





II 


Mar 


4, 1916 


I 30 


Ma. 


3 


2 





12 


Mar 


9, 1916 


2 


S. 


2 


3 






Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(v) 


by 


I 


•7 


-2.63 


-0.484 


— 0.046 


.002 


s. 


2 


.8 


2.59 


•545 


•044 


•003 


s. 


3 


I.O 


2.23 


.928 


.046 


.001 


s. 


4 


.9 


+0.12 


+0.873 


.061 


.005 


s. 


5 


.8 


0.21 


•785 


.040 


.014 


s. 


6 


•7 


0.32 


.652 


.052 


.000 


s. 


7 


.8 


0.33 


•639 


•054 


.002 


s. 


8 


.6 


0.39 


•555 


.064 


.013 


s. 


9 


.8 


+ 1.24 


-0.773 


.041 


.007 


s. 


10 


•7 


I-5I 


•971 


.030 


.001 


s. 


II 


•7 


1.65 


.991 


.022 


.008 


s. 


12 


.8 


1.70 


.984 


.031 


.001 


s. 



DETERMINATION OF PARALLAXES OF FIFTY STARS 39 







COMPARISON 


STARS. 










Depend- 






Mag- 


No. 


X 


Y ence 


Diameter 


B. D. Xo. 


nitude 


I 


-150.657 


+ 191.690 +0.404 


0.81 


+22° 735 


8.7 


3 


168.634 


-103.747 j 0.260 


0.48 


22° 732 


9.5 


4 


+ 69.087 


168.189 1 0.138 


0.63 






6 


250.202 


+ 80.245 i 0.198 


1.29 


22743 


8.0 


IT 


- 45-704 


43.186 









Nonnal : 



9.300c— 0.581/i — I.7687r= — 0.411. 
+22.523 +0.484 =+0.084. 
+5.851 =+0.017. 
M = +o".oi3±o".oo4. 
c = —o .046. 

7r = —O". 053 + 0". 009. 

p. e. -unit weight ±o".02i. 



Solution : 



B.D. + 22° 739. rTauri. {4^36^.2, + 22° 46'.) 
Mag. 4.33. ," = + 0^0004; — o".022. Spectrum A. 

The measures were in longitude. This star is a spectroscopic 
binary and is supposed to be a close binary. 

Table i. 



No. 


Date 


Hour 
angle 


Observer 


No. of 

expo- 
sures 


Quality of 
images 


No. of 
inter- 
polations 


I 
2 

3 


Jan. I, 1915 
Jan. 5, 1915 
Feb. 10, 1915 


hr. mill. 

+0 7 
46 
14 


P. 

M. 
P. 


2 

3 
3 


2 
3 

5 




I 



4 
5 
6 

7 
8 


Oct. 3, 1915 
Oct. 12, 1915 
Oct. 23, 1915 
Oct. 24, 1915 
Oct. 30, 1915 


-0 45 
15 

+0 40 
50 
5 


P. 
P. 
S. 
P. 
P. 


3 
3 
3 
3 
2 


4 
4 
2 

3 
3 









9 
10 
II 
12 


Jan. 23, 1916 
Feb. 19, 1916 
Mar. 4, 1916 
Mar. 9, 1916 


+0 20 

I 15 

1 30 

2 


s. 

Ma. 

Ma. 

S. 


2 
2 

3 
2 


3 
2 
2 

3 









Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(V) 


by 


I 


•7 


-2.63 


-0.484 


-0.049 


•005 


S. 


2 


.8 


2.59 


•545 


•030 


.014 


s. 


3 


I.O 


2.23 


.928 


•054 


.008 


s. 


4 


•9 


+0.12 


+0.873 


-•055 


.010 


s. 


5 


•9 


0.21 


.785 


.039 


.006 


s. 


6 


.7 


0.32 


.652 


.036 


.009 


s. 


7 


.8 


0.33 


•639 


.053 


.007 


s. 


8 


.8 


0.39 


•555 


•043 


.004 


s. 


9 


.8 


+ 1.24 


-0.773 


— .060 


.009 


s. 


10 


.7 


I-5I 


.971 


.056 


•005 


s. 


II 


.8 


1.65 


.991 


•034 


.018 


s. 


12 


.8 


1.70 


.984 


•057 


. . .005 


s. 



JOHN A. MILLER 



COMPARISON STARS. 









Depend- 






Mag- 


No. 


X 


Y 


ence 


Diameter 


B. D. No. 


nitude 


I 


— 172.260 


+ 165.268 


+0.293 


0.81 


+ 22° 735 


8.7 


2 


233.693 


- 35.895 


.344 


0.66 


22 730 


9.3 


5 


+177-352 


183.196 


0.207 


0.44 


22 742 


9.5 


6 


228.599 


+ 53.823 


.156 


1.29 


22 743 


8.0 


TT 


- 58.543 


6.681 











Normal equations: 



Solution : 



p. e. unit weight ±0^.030. 



9.700c- o.3i7At-i.6777r=-o.458 

+22.831 +0.381 .= —0.019 

+6.072 =+0.093 


n=-o' 
c = —0 

7r=+0' 


.007 ±0" 
.047. 
'.0I2±0" 


006. 
013. 



B. D. + 10° 654. Lalande 9091 = /3883. (^HS'^-l, + io°54'.) 
Mag. 7.9 — 7.9. 

The measures were in longitude. This is a binary star with 
a period of 16.61 years. 

Other resuks pubHshed are by FHnt (transits) and Russell 
(hypothetical). Their results are, respectively, - o".030 and 

+ 0".028. 

Table i. 



No. 


Date 


Hour 
angle 


Observer 


No. of 
expo- 
sures 


Quality of 
images 


No. of 
inter- 
polations 


I 
2 


Feb. 2, 1913 
Feb. 7, 1913 


hr. mill. 

+0 50 
6 


M. 
B. 


2 
3 


4 

5 






3 
4 


Sept. 24, 1913 
Oct. 13, 1913 


— 10 
20 


M. 

M. 


3 
3 


5 
5 


I 



5 
6 

7 


Dec. 19, 1913 
Dec. 30, 1913 
Jan. I, 1914 


-0 45 
45 
40 


S. 
P. 
P. 


3 
3 
3 


5 
5 
5 


2 

I 
I 


8 

9 
10 


Sept. 16, 1914 
Sept. 22, 1914 
Sept. 27, 1914 


— 16 
2 

+0 5 


P. 
P. 

s. 


2 
3 
3 


4 

5 
5 









DETERMINATIOX OF PARALLAXES OF FIFTY STARS 41 



Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


x\0. 


(P) 


(T) 


(P) 


(m) 


(V) 


by 


I 


.6 


-3.27 


-0.871 


— 0.014 


.008 


M. 


2 


.8 


3.22 


.909 


0.015 


.007 


M. 


3 


•7 


-0.93 


+0.941 


0.012 


•003 


M. 


4 


.6 


0.74 


•777 


0.015 


.007 


M. 


5 


.8 


-0.07 


— 0.272 


0.016 


.010 


M. 


6 


•9 


+0.04 


•450 


0.005 


.001 


H. 


7 


•9 


0.06 


.481 


O.OIO 


.004 


M. 


8 


.7 


+2.64 


+0.983 


+0.016 


.009 


M. 


9 


•9 


2.70 


•995 


0.013 


•005 


M. 


10 


.8 


2.75 


•923 


0.007 


.001 


M. 



COMPARISON STARS. 



No. 



Depend- 
ence 



Diameter 



B. D. Xo. 



Alag. 

nitude 



2 


+ 113-095 


- 53-665 


0.520 


0.76 


+ 10° 659 


9.1 


3 


24-963 


+ 19.862 


0.028 


0.37 






4 


-138.059 


33.803 


0.452 


0.50 


+ 10 652 


9-4 


TT 


2.969 


- 12.051 




0.60 







Normal equations: 

33. i47M+o.879c+9.2347r = +0.155. 
+ 7.704 +1.109 =-0.038. 
+4.728 =+0.040. 
Solution: ;u = +o".022±o".oo5. 

c= — o .006. 

7r = +0".003±0".0I4. 

p. e. unit weight zto".020. 



B.D. + 9°898. o2 0rionis. (5"^ 3i'"-4, + 9° i5'-) 
Mag. 4. 39. « = + 03.0062; — o".307. Spectrum K 

This star is measured in longitude 
proper motion. Slocum and ^Mitchell found for this star a 
parallax of o".oio. 

Table i. 



This star has large 



No. 


Date 


Hour 
angle 


Observer 


No. of 

expo- 
sures 


Quality of 
images 


No. of 

inter- 
polations 


I 
2 

3 


Oct. 13, 1913 
Oct. 22, 19 13 
Nov. 5, 19 13 


hr. min. 

+0 25 

I 15 ' 

I 


M. 

S. 
S. 


3 

3 
2 


5 
4 
4 


2 




4 
5 
6 


Feb. 26, 1914 
Mar. 4, 1914 
Mar. 20, 1914 


+0 40 

10 

I 40 


M. 

P. 

P. 


3 
3 

2 


4 
5 
2 


I 


I 


7 
8 

9 


Sept. 25, 1914 
Sept. 28, 1914 
Mar. 30, 1914 


-0 30 
+0 17 

20 


S. 
P. 
M. 


3 
2 

2 


5 

5. 
5 


I 




10 
II 
12 


Feb. 8, 1915 
Feb. 10, 1915 
Feb. 19, 1915 


+0 6 

35 
32 


P. 
P. 
P. 


3 
3 
2 


5 
5 
4 




2 




Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(V) 


by 


I 


•9 


-2.48 


+0.885 


-0.185 


-005 


P. 


2 


-9 


2.39 


.800 


•195 


.005 


P. 


3 


.8 


2.25 


.632 


.191 


.001 


P. 


4 


I.O 


— 1. 12 


-0.955 


.202 


.007 


P. 


5 


I.O 


1.06 


-979 


.189 


•005 


P. 


6 


.8 


0.90 


.990 


.188 


-005 


P. 


7 


.9 


+ 0.99 


+0.989 


.176 


.004 


P. 


8 


-9 


1.02 


.978 


.168 


.005 


P. 


9 


-7 


1.04 


•969 


.171 


.001 


P. 


10 


I.O 


+2-35 


-0.821 


.181 


.005 


P. 


II 


.8 


2.37 


.840 


.171 


.005 


P. 


12 


•7 


2.46 


-913 


-175 


.001 


P. 







COMPARISON 


STARS. 






No. 


X 


F 


Depend- 
ence 


Diameter 


B. D. No. 


Mag- 
nitude 


2 
8 

10 
II 

TT 


+ 184.594 

-238-599 
174.614 

+ 228.620 

0-939 


+ 93-140 
181.937 

-149.867 
125.209 

+ 27.742 


+0.297 
0.301 
0-183 
0.219 


0.70 
0.42 
0-63 
0.65 

0.68 







Normal equations : 

10.400C— o.578Ai — o.3877r= —1.906. 
+34.581 -4.626 =+0.250. 
+8.475 =+0.097. 
Solution: ^i = +0". 023^=0". 003. 

c = — o .183. 
7r = +0". 027 ±0". 006. 
p. c. unit weightdbo".oi5. 



B.D. +27°ii64. 02149. i6^30^.2, + 27°22\) 
Mag. 6.9 — 9.4. 

The measures were in longitude. This star is probably a 
binary with slow angular motion. No orbit has been computed 
for it. No other parallax has been published for this star. 

Table i. — ~ 



No. 


Date 


Hour 
angle 


Observer 


No. of 
expo- 
sures 


Quality of 
images 


No. of 
inter- 
polations 


I 
2 


Oct. 28, 1913 
Nov. I, 1913 


hr. min. 
+ 23 
— 10 


P. 

s. 


3 

3 


5 
3 




I 


3 
4 


Mar. 3, 1914 
Mar. 15, 1914 


+ 1 15 
I 25 


M. 
M. 


3 
2 


5 
5 


I 
I 


5 
6 

7 


Oct. 31, 1914 
Nov. 2, 1914 
Nov. 13, 1914 


+ 1 

25 

1 


M. 
M. 
M. 


3 
2 

3 


3 
5 
5 







8 

9 
10 
II 


Feb. 19, 1915 
Feb. 21, 1915 
Feb. 28, 1914 
Mar. 4, 1915 


+0 36 

25 
20 
50 


P. 

M. 
M. 
M. 


2 
2 

3 

2 


5 
4 
2 

5 




I 

3 




Table 2. 



Weight 
of plate 

(P) 



Time in 
100 davs 

(T)' 



Parallax 
factor 

(P) 



Solution 
(m) 



Residual 

(V) 



Measured 
bv 



I 


•9 


-3.02 


+0.873 


+0.033 


.005 


P. 


2 


•7 


2.98 


.838 


.028 


.010 


P. 


3 


•9 


-1.76 


-0.904 


.026 


•005 


P. 


4 


.8 


1.64 


.972 


.028 


.008 


P. 


5 


.9 


+0.66 


+0.849 


.059 


.018 


P. 


6 


.8 


0.68 


.830 


.044 


.004 


P. 


7 


I.O 


0.79 


-709 


.029 


.010 


P. 


7 


.7 


+ 1-77 


-0.794 


.023 


.001 


P. 


9 


.8 


1.79 


.815 


.027 


-003 


P. 


10 


•9 


1.86 


-879 


.027 


-003 ! 


P. 


II 


•7 


1.90 


-909 


.006 


.018 


P. 



Normal equations: 



Solution 



p. e. unit weight =i=o".03: 



9.100C— o.097/i — o.7i77r = +0.292. 
+31.147 -4.730 =-0.026. 
+6.619 =+0.041. 
n = +0". 004=^0". 005. 
c = +o .031. 

TT = +0^.048 ±0". 013. 







COMPARISON 


STARS. 






No. 


A 


Depend- 
Y ence 


Diameter 


B. D. Xo. 


Mag- 
nitude 


2 

5 

9 

10 


+ 152.502 

— 160.040 

169.792 

+ 177-331 

5-090 


+ 81.341 

31-649 

— 129.926 

+ 16.934 
77-225 


+ 0.437 
0.638 

-0.155 
+0.080 


0.75 
0.64 
0.46 

0.57 
0.71 


+27° II72 
+ 27° II74 


9-1 
9-5 



B. D. — 0° 1462. Lalande 13198. (6*^ 45'"-7, — 0° 25'.) 
Mag. 5.83. M = + o^oco5; — o".i75. Spectrum A. 

This star is measured in longitude. Flint (transits) found 
a parallax of +©".25 for this star. 

Table i. 















No. of 




No. of 








Hour 




expo- 


Quality of 


inter- 


No. 




Date 


angle 


Observer 


sures 


images 


polations 








hr. ynin. 










I 


Oct. 


16, 1912 


+ 





M. 


2 


2 


3 


2 


Oct. 


20, 1912 





6 


B. 


2 


I 


2 


3 


Nov. 


26, 1912 





12 


B. 


2 


I 





4 


Feb. 


18, I913 


+ 





M. 


2 


2 


2 


5 


Feb. 


23. 1913 





15 


AI. 


2 


3 


3 


6 


Mar. 


2, I913 





55 


M. 


2 


4 


I 


7 


Nov. 


2, I9I3 


+ 


23 


P. 


3 


4 


4 


8 


Nov. 


17, I9I3 


I 





M. 


2 


5 


I 


9 


Nov. 


20, I913 





20 


P. 


3 


5 





10 


Dec. 


4, 1913 





30 


P. 


3 


3 





II 


Dec. 


II, I9I3 


I 


10 


P. 


2 


5 





12 


Feb. 


25, I9I4 


+ 


8 


P. 


3 


2 


3 


13 


Mar. 


4. I9I4 





23 


P. 


2 


5 





14 


Mar. 


12, I9I4 


I 


3 


M. 


3 


5 






44 



JOHN A. MILLER 



Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(v) 


by 


I 


.6 


-2.58 


+ 0.978 


+ 2.735 


.009 


M. 


2 


.6 


2.54 


.961 


.727 


.001 


M. 


3 


.7 


2.17 


.607 


.727 


.002 


M. 


4 


.6 


-1.33 


-0.725 


.717 


.003 


P. 


5 


.6 


1.28 


.782 


•713 


.007 


P. 


6 


.8 


1. 21 


.852 


•725 


.006 


S. 


7 


.8 


+ 1.24 


+0.878 


.721 


.004 


M. 


8 


.8 


1.39 


.725 


•715 


.009 


M. 


9 


•9 


1.42 


.689 


.727 


.003 


S. 


10 


•9 


1.56 


•494 


.728 


.005 


M. 


II 


•7 


1.63 


.384 


.723 


.001 


M. 


12 


.8 


+2.39 


— 0.801 


.714 


.004 


S. 


13 


.7 


2.46 


.868 


.731 


.013 


M. 


14 


•7 


2.54 


.928 


.721 


.003 


M. 



COMPARISON STARS. 









Depend- 






Mag- 


No. 


X 


Y 


ence 


Diameter 


B. D. No. 


nitude 


I 


- 95-826 


+ 34.862 


+ 0.15 


0.87 


-0° 1455 


8.8 


2 


87-309 


123-598 


0.14 


0.61 


-0° 1457 


9-3 


5 


+ 34-863 


-218.493 


0.16 


0.80 


-0° 1464 


9.0 


7 


-132.556 


+ 190.926 


0.14 


0.57 


-0° 1454 


9-5 


12 


+217.746 


-184.809 


0.14 


0.57 


-0° 1467 


9.0 


13 


351.762 


+ 46.669 


O.IO 


0.64 


-0° 1471 


9-3 


14 


— 288.677 


7.249 


0.17 


0.48 






X 


20.263 


- 6.838 




0.76 







Normal equations : 



Solution ; 



36.36: 



:m+ 4-209C 
+ 10.206 



p. e. unit weight =to".oi9. 



— o .002 

+2 .722 
+o".oi5 



-0.720 

+6.085 

o" 



r = 11.440. 

= 27.785- 
= 1.980. 

,003. 
.008. 



Nova Geminorum No. 2, 1912. (6^ 49.°^ 3, + 32° 15'.) 
Mag. var. Spectrum Nova. 

The measures were in longitude. Slocum and Mitchell found 
the parallax to be + o".oo6. 



DETERMINATION OF PARALLAXES OF FIFTY STARS 45 



Table i. 













No. of 




No. of 






Hour 


1 


expo- 


Quality of 


inter- 


No. 


Date 


angle 


Observer 


sures 


images 


polations 






hr. 


min. 










I 


Mar. i8, 1912 


+0 


12 


B. 


3 


2 





2 


Mar. 22, 19 12 





30 


B. 


3 


I 





3 


Mar. 30, 19 12 


I 


12 


B. 


3 


2 





4 


Oct. 15, 1912 


+ 


42 


B. 


3 


I 





5 


Oct. 16, 1912 








M. 


2 


3 


2 


6 


Oct. 17, 1912 


— 


42 


B. 


3 


5 





7 


Oct. 20, 1912 





54 


B. 


3 


2 


I 


8 


Nov. 18, 1912 


+0 





^I. 


3 


3 





9 


Nov. 19, 1912 


— 


18 


B. 


3 


3 


2 


10 


Feb. 10, 1913 


— 


18 


B. 


3 


5 





II 


Feb. 13, 1913 


+ 





^I. 


3 


3 


I 


12 


Mar. 5, 19 13 








B. 


3 


5 


I 


13 


Mar. 12, 1913 





18 


B. 


3 


3 





14 


Nov. I, 1913 


+ 1 





M. 


3 


3 


2 



Table i 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(V) 


by 


I 


•7 


-2.89 


-0.972 


+0.313 


.019 


M. 


2 


.7 


2.85 


.986 


.338 


.006 


S. 


3 


•7 


2.77 


1. 000 


.358 


.026 


M. 


4 


•9 


-0.78 


+0.974 


.334 


.012 


S. 


5 


.8 


0.77 


.970 


.321 


.001 


S. 


6 


•5 


0.76 


.966 


.302 


.020 


S. • 


7 


•5 


0.73 


•951 


.327 


.005 


M. 


8 


•9 


0.44 


.717 


•317 


.005 


S. 


9 


•9 


0.43 


.672 


.314 


.008 


s. 


ID 


•5 


+0.40 


-0.651 


•325 


.003 


M. 


II 


.9 


0.43 


.690 


.331 


.003 


S. 


12 


•7 


0.63 


.894 


.322 


.006 


S. 


13 


.6 


0.70 


.942 


•319 


.009 


M 


14 


.7 


+3-04 


+0.869 


.331 


.012 


S. 



COMPARISON STARS. 



No. 


X 


Y 


Depend- 
ence 


Diameter 


B. D. No. 


Mag- 
nitude. 


2 

3 
6 

■K 


-134-532 
136.549 

+271.081 

32.650 


+ 51-185 

- 21.534 

29.651 


+0.87 
-0.28 
+0.41 


0.38 

0.43 
0.32 
0.40 


+32° 1422 


9.2 



Normal equations: 



Solution: 



26.i20yu— 5.229c +4. 0007r= —1.744. 
+ 10.009 +0.256 =+3.258. 
+7.701 =+0.048. 



p. e. unit weight =to".o35 



M=-o".oo5 
c = +o .325 

TV 



o".oo8. 
= — o".oi9=to".oi3. 



46 



JOHN A. MILLER 



B. D. + 20° 1687. s Geminorum. (6^^ 58°^.i, + 20° 4i'.8.) 

Mag. var. fJ- — 0^0003; — o".oo8. Spectrum G. _™, 

The measures were in longitude. This star is a spectroscopic 
binary. No other parallax has been published. 

Table i. 











No. of 




No. of 






Hour 




expo- 


Quality of 


inter- 


No. 


Date 


angle 


Observer 


sures 


images 


polations 






hr. min. 










I 


Mar. 8, 1915 


+0 7 


P. 


2 


3 





2 


Mar. 14, 1915 


45 


M. 


3 


3 





3 


Mar. 16, 1915 


50 


M. 


3 


3 





4 


Oct. II, 1915 


+0 30 


M. 


2 


4 





S 


Oct. 12, 1915 


37 


P. 


2 


2 





6 


Oct. 24, 1915 


-0 48 


P. 


3 


4 





7 


Nov. 9, 1915 


15 


P. 


3 


3 





8 


Nov. 24, 1915 


+ 1 40 


M. 


3 


3 





9 


Nov. 2j, 1915 





M. 


2 


3 





10 


Mar. 4, 1916 


+0 20 


Ma. 


2 


3 





II 


Mar. 9, 1916 


30 


S. 


3 


5 





12 


Mar. II, 1916 


40 


Ma. 


3 


3 






Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(v) 


by 


I 


.8 


— 2.12 


-0.889 


+ 0.108 


.005 


s. 


2 


.8 


2.06 


.931 


.099 


.004 


s. 


•3 


.8 


2.04 


.944 


.103 


.000 


s. 


4 


.8 


+ 0.05 


+0.995 


+ .106 


.003 


s. 


5 


.7 


0.06 


.993 


.113 


.004 


s. 


6 


.9 


0.18 


.950 


.103 


.005 


s. 


7 


.8 


0.34 


.829 


.110 


.002 


s. 


8 


•9 


0.49 


.657 


.115 


.008 


s. 


9 


.8 


0.52 


.615 


.103 


.004 


s. 


10 


.8 


+ 1.50 


-0.862 


+ .097 


.004 


s. 


II 


i.o 


1-55 


•903 


.112 


.Oil 


s. 


12 


.7 


1-57 


.918 


.092 


.009 


s. 







COMPARISON 


STARS. 












Depend- 






Mag- 


No. 


X 


Y 


ence 


Diameter 


B. D. No. 


nitude 


3 


-173-737 


+ 86.386 


+0.333 


0.78 


+ 20° 1678 


9.1 


4 


216.128 


- 47.678 


0.130 


9-54 






10 


+ 174-059 


+ 91-434 


0.423 


0.61 






13 


215.807 


-130.144 


O.II4 


0.55 






IT 


12.386 


+ 46-326 




0.76 







Normal equations: 



Solution : 



p. e. unit weight 



9.800C+ o.246M-o.3557r= +1.032. 
+ 16.806 +2.146 =+0.026. 
+7.574 =-o.oii. 
/U = — 0".002 =to".oi5. 
<; = +o .105. 
= +o".oi7 ±o",oo7. 
= o".oi9. 



DETERMINATION OF PARALLAXES OF FIFTY STARS 47 



B. D. + 21° 1528. Lalande 13849. 7^4^.2, + 21° 25'.) 
Mag. 6.46. w =— 0^0120; — 0^.482. Spectrum Fg. 
The measures are in longitude. Chase, with the hehometer, 
found a parallax for this star of +o".io, and Adams found a 
hypothetical parallax of +o".03. ■ 

Table i. 













No. of 




No. of 








Hour 




expo- 


Quality of 


inter- 


No- 




Date 


angle 


Observer 


sures 


images 


polations 








hi', mill. 










I 


Nov. 


2. I9I3 


+0 56 


P. 


3 


5 





2 


Nov. 


6, 1913 


42 


P. 


3 


3 





3 


Dec. 


9. 1913 


45 


P. 


3 


5 





4 


Feb. 


26, 1914 


+0 50 


M. 


2 


5 





5 


Mar. 


4. 1914 


49 


P. 


3 


5 


I 


6 


Oct. 


28, 1914 


+0 25 


M. 


3 


4 


I 


7 


Nov. 


2, 1914 


50 


M. 


3 


4 





8 


Nov. 


9. 1914 


I 


M. 


3 


3 





9 


Feb. 


10, 1915 


+0 


P. 


3 


5 





10 


Feb. 


28, 1915 


50 


M. 


3 


3 


I 


II 


Mar. 


I, 1915 


-0 15 


P. 


3 


3 





12 


Mar. 


12, 1915 


+0 5 


P. 


3 


5 












Table 2. 










Weight 


Time in 


Parallax 










of plate 


100 days 


factor Solu 


tion 


Residual 


Measured 


No. 


(P) 


(T) 


(P) (r 


n) 


(v) 


by 


I 


•9 


-2.75 


+0.897 +0 


138 


.005 


H. 


2 


.8 


2.71 


.864 


133 


.000 


H. 


3 


•9 


2.38 


•454 


133 


.006 


H. 


4 


.8 


-1-59 


-0.786 


095 


.020 


H. 


5 


.9 


1-53 


.846 


118 


•005 


H. 


6 


I.O 


+0.85 


+0.933 


096 


.003 


H. 


7 


.9 


0.90 


.899 


095 


.004 


H. 


8 


•9 


0.97 


•839 


090 


.007 


H. 


9 


•9 


+ 1.90 


-0.583 


084 


.001 


H. 


10 


•9 


2.08 


.805 


088 


.008 


H. 


II 


.9 


2.09 


.815 


085 


.005 


H. 


12 


1.0 


2.20 


.910 


.074 


.004 


H. 







COMPARISON 


STARS. 












Depend- 






Mag- 


No. 


A' 


Y 


ence 


Diameter 


B. D. No. 


nitude. 


3 


+ 205.487 


+ 57-995 


+0.060 


0.83 






5 


-173.803 


-183.690 


0.256 


0.84 


+ 21 °I524 


9.0 


6 


93.691 


143.858 


0.202 


0.57 






II 


+ 62.007 


+269.551 


0.482 


0.61 


+ 21° I53I 


9.4 


TT 


-21.132 


57-263 




0.76 







Normal equations: 

10. 800*;+ 0. 762^+0. I207r = +i.l0I. 
+40.121 —6.689 = —0.327. 
+ 7.192 =+0.105. 
SolutioR-: M= —o". 044*0". 004. 

c = +o .103. 
TT = +o".oi9 ±o".oio. 
p. e. unit weight =to".026. 



48 



JOHN A. MILLER 



B. D. + 5° 1739. aCanis Minoris = Procyon. (7'^34™.i, + 5°29'.) 
Mag. 0.5 - 13.5. H- = — 0^0466; - I ".030. Spectrum F5. 

The measures were in longitude. The star was chosen be- 
cause it is a binary, and because the parallaxes determined for 
it are discordant, but chiefly because we wished to see what we 
could do with stars as bright as Procyon. The occulting disk 
was set so that about o.oi of the light of the star reached the 
plate. 

Kapteyn, from Auwer's, Flint's and Elkins's measures, de- 
cided the absolute parallax of this star was + 0^.324. Adams 
computed a hypothetical parallax of +o".36 for it, and Russell 
a hypothetical parallax of +o".26^. 

Table i. 



No. 


Date 


Hour 
angle 


Observer 


No. of 
expo- 
sures 


Quality of 
images 


No. of 
inter- 
polations 


I 
2 


Feb. 23, 1913 
Mar. 25, 1913 


hr. min. 
+ 00 

50 


M. 
M. 


3 

2 


2 
2 


I 



3 
4 


Oct. 2^, 1913 
Dec. 4, 1913 


+ 
12 


P. 
P. 


2 
2 


4 

I 


I 
2 


5 
6 

7 


Mar. 12, 1914 
Mar. 13, 1914 
Mar. 22, 19 14 


+0 55 

43 


M. 
P. 
M. 


3 
2 

3 


5 

5 
5 


I 
I 

I 


8 

9 
10 
II 


Nov. 2, 1914 
Nov. II, 1914 
Nov. 17, 1914 
Nov. 20, 1914 


+ 1 
I 

-0 14 
30 


M. 
M. 
P. 
M. 


2 
3 
3 
2 


3 
2 

5 
3 





I 





Table 2. 



No. 


Weight 
of plate 
(P) 


Time in 

100 days 

(T) 


Parallax 

factor 

(P) 


Solution 
(m) 


Residual 

(V) 


Measured 
by 


I 

2 


•9 

•7 


-3-84 

3-54 


— 0.640 

•939 


+0.429 
•392 


.006 
.002 


P. 
P. 


3 

4 


•7 
.6 


-1-37 
1. 00 


+0.976 
•659 


.389 
•351 


.006 
.005 


P. 
P. 


5 
6 

7 


.9 

•7 
•9 


— 0.02 

O.OI 

+0.08 


-0.834 
.844 
.918 


,214 
.206 
.207 


.001 
.008 
.002 


P. 
P. 
P. 


8 

9 
10 
II 


.8 
•9 
•9 

.7 


+2.33 
2.42 
2.48 
2.51 


+0.955 
.900 

.851 
.823 


.214 
.209 
.184 
.177 


.010 
.013 
.006 
.009 


P. 
P. 
P. 
P. 



DETERMINATION OF PARALLAXES OF FIFTY STARS 49 



COMPARISON STARS. 









Depend- 






Mag- 


No. 


X 


F 


ence 


Diameter 


B. D.No. 


nitude. 


2 


- 1 7544 1 


- 20.185 


+0.122 


0.51 






3 


131-243 


32.073 


0.146 


0.42 


+5° 1736 


9-1 


4 


202.387 


125.172 


O.I9I 


0.56 






6 


+ 151-588 


+ 36.117 


O.I9I 


1-54 


+5° 1742 


7-5 


7 


150795 


73-465 


0.163 


0.70 


+5° 1743 


9.1 


8 


206.690 


67.845 


0.187 


0.58 


+5° 1744 


9-1 


n 


14.196 


0.591 




1-35 







Normal equations: 



Solution: 



.700C+ 0.585A1+ 0.593-= +2.315. 

+43.522 +10.247 =-1.450. 

+ 6.380 =+0.022. 



p. e. unit weight ='=o".024. 



//= — o '.241 ±0 .005. 

c=+o .265. 

7r = +o".287=t=o".OI2. 



B. D. + 2° 1854. 13 Canis Minoris {-j^ SJ^.i, + 2° 36'.) 
Mag. 4.52. // = — 0^0026; + o".099. Spectrum K. 

The measures are in longitude. No other parallax of this 
star has been published. 



Table 











No. of 




No. of 






Hour 




expo- 


Quality of 


mter- 


No. 


Date 


angle 


Observer 


sures 


images 


polations 






hr. min- 










I 


Nov. 5, 1913 


+0 30 


S. 


3 


5 





2 


Nov. 20, 1913 


8 


P. 


3 


5 





3 


Dec. 4, 1913 


45 


P. 


3 


5 





4 


Dec. 19, 1913 


30 


s. 


2 


3 





5 


Mar. 3, 1914 


+ 1 


M. 


3 


4 





6 


Mar. 20, 1914 


40 


P. 


3 


5 





7 


Mar. 22, 19 14 


I 15 


M. 


3 


3 





8 


Nov. 13, 1914 


+0 45 


M. 


3 


4 





9 


Nov. 17, 1914 


20 


P. 


3 


5 





10 


Nov. 20, 1914 


-0 5 


M. 


3 


5 





II 


Feb. 10, 1915 


+0 5 


P. 




5 





12 


Feb. 21, 1915 


7 


M. 


^ 


2 





13 


Mar. 26, 1915 


-0 15 


P. 


2 


3 





14 


Mar. 27, 1915 


+ 1 


Ma. 


2 


3 






50 



JOHN A. MILLER 



Table 2. 





Weight 


Time in 


Parallax 










of plate 
(P) 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(T) 


(P) 


(m) 


(v) 


by 


I 


•9 


-2.54 


+0.968 


-0.045 


.003 


P. 


2 


.8 


2.39 


.877 


.052 


.009 


P. 


3 


I.O 


2.25 


'737 


.035 


.010 


P. 


4 


.8 


2.10 


•539 


.059 


.Oil 


P. 


5 


•9 


-1.36 


-0.659 


.057 


.004 


P. 


6 


.9 


1. 19 


.850 


.063 


.000 


P. 


7 


•7 


1. 17 


.859 


. -053 


.010 


P. 


8 


1.0 


+ I.I9 


+0.929 


•058 


.004 


P. 


9 


1.0 


1.23 


.902 


.062 


.001 


P. 


10 


•9 


1.26 


.879 


.061 


.002 


P. 


II 


.8 


+ 2.08 


-0.342 


.066 


.oil 


P. 


12 


.8 


2.19 


•515 


.080 


.001 


P. 


13 


•7 


2.52 


.898 


.090 


.006 


P. 


14 


.8 


2.53 


.906 


.092 


.008 


P. 



COMPARISON STARS. 









Depend- 






Mag- 


No. 


^ 


Y 


ence 


Diameter 


B. D. No. 


nitude 


2 


+ 254.050 


- 90.326 


+0.159 


0.90 


+2° 1862 


8.6 


5 


-175.155 


+ 200.254 


0.254 


0.62 






6 


III. 616 


144-253 


0.246 


0.53 


2° 1850 


9.4 


10 


+ 32.720 


-254.180 


0.341 


0.61 


3° 1877 


9.0 


TT 


- 20.445 


14.782 




0.77 







Normal equations: 



Solution : 



1 2. 000c— o.484/i + i.3647r= —0.739. 
+44.086 -5.713 =-0.249. 
+7.691 =+0.003. 



p. e. unit weight ±0. "022. 



M==-o".025: 
c = — o .063. 

7r=+o".035 



o .003. 
^o".oo8. 



B. D. + 12° 1759. /3581. (7^ 58-8, + 12° 35'.) 
Mag. 8.7 — 8.7. /^ ^ + 0.^0053; — o".ii8. 

The measures are in longitude. This star is a close binary, 
the components of which are of the same magnitude. They are 
so close that it was impossible to separate their images on the 
plate. In fact, the combined image of the stars was not sensibly 
elongated. In the measurement the combined image of the 
parallax star was bisected. No other parallax of this star has 
been published. 



DETERMINATION OF PARALLAXES OF FIFTY STARS 51 



Table 



No. 


Date 


Hour 

angle 


Observer 


No. of 
expo- 
sures 


Quality of 
images 


No. of 
inter- 
polations 


I 
2 

3 


Mar. 4, 19 15 
Mar. 8, 1915 
Mar. 12, 1915 


hr . min. 
+0 12 
-0 6 
+ 


M. • 

P. 

P. 


2 

3 
3 


4 
4 
I 







4 
5 
6 

7 
8 

9 


Oct. 24, 1915 
Nov. 13, 1915 
Nov. 27, 1915 
Dec. 4, 1915 
Dec. 10, 1915 
Dec. 14, 1915 


+0 15 

20 

1 
— 20 

+0 15 

10 


P. 

M. 

M. 

M. 

Ma. 

P. 


3 
2 

3 
3 
2 

3 


3 
4 
4 
3 
4 
3 


3 
I 






10 


Mar. 4, 1916 


+ 1 3 


Ma. 


2 


2-3 


I 


II 
12 


Mar. 9, 1916 
Mar. II, 1916 


40 
31 


S. 
Ma. 


3 
3 


4 
3 







Table 2. 



No. 


Weight 

of plate 

(P) 


Time in 

100 days 

(T) 


Parallax 

factor 

(P) 


Solution 
(m) 


Residual 
(v) 


Measured 
by 


I 


•9 


-2.27 


— 0.690 


+0.165 


.006 


s. 


2 


•9 


2.23 


.737 


.175 


.004 


s. 


3 


.7 


2.19 


•783 


.172 


.001 


s. 


4 


,8 


+0.07 


+0.994 


.227 


.006 


s. 


5 


•9 


0.27 


.920 


•245 


.100 


s. 


6 


•9 


0.41 


.800 


.226 


.009 


s. 


7 


.9 


0.48 


.721 


.242 


.007 


s. 


8 


I.O 


0.54 


.646 


-233 


.001 


s. 


9 


.8 


0.58 


•593 


.226 


.007 


s. 


10 


•7 


+ 1-39 


-0.698 


.220 


.002 


s. 


II 


1.0 


1.44 


.758 


.228 


.006 


s. 


12 


•9 


1.46 


.780 


.215 


.006 


s. 







COMPARISON 


STARS. 














Depend- 








Mag- 


No. 


X 


^ 


ence 


Diameter 


B. D. 


No. 


nitude 


4 


+ 177-112 


- 52.255 


+0.108 


0.71 








6 


262.245 


+ 46.985 


0.348 


0.62 








13 


— 196.042 


52.371 


0-394 


0.70 


+ 12° 


1753 


9.3 


15 


-243-314 


- 47-103 


0.150 


0.51 








TT 


-3.122 


+ 24.255 




0.89 









Normal equations; 



Solution : 



10.400C+ 0.248M+0.331X =2.241. 

+ 18.804 +2.803 =0.364. 

+6.104 =0.217. 



p. e. unit weight ±o".02i, 



^+o".o65 = 
^+0 .215. 
= +o".o82 = 



= o".oo5. 



= .009, 



52 



JOHN A. MILLER 



B. D. + i8° 1867. CCancri = 2 1196. (S^^ 6^^. 5, + 17° 57'.) 
Mag. 6.02. fjL = +0^0046 — o".i40. Spectrum F. 

This is a wide visual double star, consisting of a large com- 
ponent A and a slightly fainter component BC. The latter is a 
binary with a period of 60.083 years. The combined image of 
the components of BC is sensibly round, and in the measures 
was bisected. The same set of plates and the same comparison 
stars were used for the A- and the jBC-components, and the ob- 
servational data for both are found in Table i. Table 2 con- 
tains the solution for the ^-component, and Table 3 the solution 
for the 5C-component. 

Russell finds a hypothetical parallax for the 5C-component 
of + o".045. 

Table i. 













No. of 




No. of 








Hour 




expo- 


Quality of 


inter- 


No. 




Date 


angle 


Observer 


sures 


images 


polations 








hr. mill. 










I 


Nov. 


I, I913 


+ 20 


M. 


2 


3 





2 


Nov. 


4, 1913 


37 


P. 


3 


5 





3 


Nov. 


17, 1913 


45 


M. 


3 


4 





4 


Nov. 


20, 1913 


50 


P. 


3 


5 


I 


5 


Dec. 


9, 1913 


40 


P. 


2 


3 





6 


Mar. 


12, 1914 


+ 1 20 


M. 


3 


5 





7 


Mar. 


13, 1914 


15 


P. 


3 


3 





8 


Apr. 


5. 1914 


55 


S. 


2 


2 





9 


Apr. 


9, 1914 


I 10 


M. 


2 


5 





10 


Apr. 


10, 1914 


I 20 


S. 


3 


5 





II 


Apr. 


12, 1914 


I 20 


M. 


3 


- 4 





12 


Nov. 


13, 1914 


+ 1 10 


M. 


2 


2 


I 


13 


Nov. 


20, 1914 


55 


M. 


2 


3 






Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(v) 


by 


I 


.8 


-1-34 


+ 0.979 


-0.128 


.003 


s. 


2 


.9 


1.31 


.968 


.112 


.012 


s. 


3 


•7 


1. 18 


.893 


.132 


.008 


M. 


4 


•9 


I-I5 


.869 


.125 


.000 


M. 


5 


•7 


0.96 


.664 


.128 


.003 


M. 


6 


•9 


-0.03 


-0.779 


.124 


.006 


S. 


7 


.9 


0.02 


.790 


.128 


.002 


S. 


8 


.8 


+0.21 


.968 


.136 


.006 


s. 


9 


•7 


0.25 


.984 


.124 


.006 


M. 


10 


.9 


0.26 


.988 


.131 


.001 


s. 


II 


.7 


0.28 


•994 


.134 


.004 


M. 


12 


.6 


+2.43 


+0.923 


.116 


.007 


M. 


13 


•7 


2.50 


.871 


.101 


.008 


M. 



DETERMINATION OF PARALLAXES OF FIFTY STARS 53 



COMPARISON STARS FOR BOTH COMPONENTS. 









Depend- 






Mag- 


No. 


X 


Y 


ence 


Diameter 


B. D. No. 


nitude 


I 


- 3-510 


+ 118.206 


0.234 


0.25 






2 


159-652 


70.254 


0.182 


0.33 


+ 18° 1864 


9-5 


3 


222.282 


- 1.988 


O.I3I 


0.39 


1863 


9-5 


4 


+ 52.489 


+ 30.787 


0.193 


0.55 


1870 


9-1 


5 


133-446 


- 29.932 


0.170 


0.29 


1874 


9-5 


7 


199.506 


187.330 


0.090 


0.51 


1877 


9-3 


7T 


- 8.335 


+ 24.256 




0.54 







Normal equations: 

Solution : 

p. e. unit weight 



[O.200C— o.843/i+o.2307r= —1.274. 

+ 13-905 -2.129 =+0.149. 

+8.304 =+0.015. 

M = +0". 019 ±0". 005. 
c=-o .125. 
= +0". 030^0". 007. 



^o '.019. 



Table 3. 





Weight 


[ 






Resid- 






of plate 


1 Time in lOO days 


Parallax factor 


Solution 


ual 




No. 


(P3 


! (T^ 


(P) 


(m) 


(v) 


Measured by 


I 


•7 


1 

iSame as Table 2 


Same as Table 2 


+ 0.050 


.012 


Same as Table 2 


2 


.9 


Same as Table 2 


Same as Table 2 


-038 


.000 


Same as Table 2 


3 


.7 


iSame as Table 2 


Same as Table 2 


.035 


.004 


Same as Table 2 


4 


.7 


ISame as Table 2 


Same as Table 2 


•045 


.006 


Same as Table 2 


5 


•7 


Same as Table 2 


Same as Table 2 


.031 


.008 


Same as Table 2 


6 


•9 


jSame as Table 2 


Same as Table 2 


.026 


.010 


Same as Table 2 


7 


-9 


ISame as Table 2 


Same as Table 2 


.047 


.0X1 


Same as Table 2 


8 


.7 


Same as Table 2 


Same as Table 2 


.032 


-005 


Same as Table 2 


Q 


.8 


Same as Table 2 


Same as Table 2 


.020 


.017 


Same as Table 2 


ID 


■9 


Same as Table 2 


Same as Table 2 


.049 


.012 


Same as Table 2 


II 


•9 


Same as Table 2 


Same as Table 2 


•045 


.008 


Same as Table 2 


12 


.6 


Same as Table 2 


Same as Table 2 


•059 


.010 


Same as Table 2 


13 


•7 


Same as Table 2 

1 


Same as Table 2 


.078 


.009 


Same as Table 2 



Normal equations: 



Solution : 



lo.iooc— o.424yu — o.2437r = 0.422. 

+ 13.478 -1.857 =0.079. 

+8.258 =0.036. 



p. e. unit weight ±0^.030. 



ij. = +0". 039 ±0". 008. 
c = +0 .042. 

7r=+0".035±0".0II 



B. D. — 12° 2449. Lalande 16304. (8*^ i3"'.7, — 12° 18'.) 
Mag. 6.04. /" = + 0^0191; — o".99i. Spectrum F. 

The measurements are in longitude. 

Chase obtained for this star a parallax of o".095 ^^^ Flint a 
parallax of o". 12. 

Table i. 











No. of 




No. of 






Hour 




expo- 


Quality of 


inter- 


No. 


Date 


angle 


Observer 


sures 


images 


polations 






hr. min. 










I 


Mar. 5, 1913 


+0 30 


B. 


3 


I 


2 


2 


Mar. 22, 1913 


10 


M. 


3 


I 





3 


Nov. 24, 1913 


+ 1 10 


M. 


3 


I 


2 


4 


Dec. 5, 1933 


40 


S. 


3 


I 


I 


5 


Dec. 29, 1913 


45 


P. 


3 


2 





6 


Mar. 13, 1914 


+0 52 


P. 


3 


5 


I 


7 


Apr. 5, 1914 


I 7 


s. 


3 


5 





8 


Mar. I, 1915 


— 42 


p. 


3 


2 





9 


Apr. 15, 1915 


+ 1 30 


M. 


3 


3 


2 


10 


Nov. 24, 1915 


+2 


M. 


3 


3 


I 


II 


Nov. 29, 1915 


40 


S. 


3 


3 





12 


Dec. 4, 1915 


30 


M. 


3 


3 


I 









Table 


2. 






No. 


Weight 

of plate 

(P) 


Time in 

100 days 

(T) 


Parallax 
factor 
(P) 


Solution 
(m) 


Residual 

(v) 


Measured 
by 


I 

2 


.6 

•5 


-5.10 

4^93 


-0.412 
.659 


-0.326 
•324 


.001 
.002 


s. 

H. 


3 
4 
5 


I.O 

.7 
.8 


— 2.46 

2.35 
2. II 


+0.965 

•905 
•663 


.223 

•237 
.214 


.004 
.012 
.006 


S. 

s. 

s. 


6 

7 


1.0 
1.0 


-i^37 
1. 14 


-0.531 
.820 


.222 
.212 


.004 
.004 


s. 
s. 


8 
9 


.8 
•9 


+2.16 
2.61 


-0.338 
.906 


•113 
.107 


.003 
.001 


s. 
s. 


10 
II 
12 


.8 
.8 
.8 


+4.84 
4.89 
4.94 


+0.954 

•944 
•915 


.014 
.005 
.006 


.003 
.004 
.002 


s. 
s. 

s. 





COMPARISON STARS FOR BOTH COMPONENTS. 










Depend- 






Mag- 


No. 


X 


Y 


ence 


Diameter 


B. D. No. 


nitude 


t 


+ 298.764 


+ 118.099 


0.239 


0.62 


-12° 2454 


lO.O 


2 


297.190 


-103-739 


0.198 


0.49 






3 


-146.182 


146.354 


0.165 


0.57 






4 


248.829 


+ 41-636 


0.193 


0.64 


12° 2436 


9.0 


6 


200.94 1 


90.356 


0.205 


0.50 


12° 2437 


9.5 


TT 


+ 16.687 


10.153 




0.63 







Normal equations: 



9.700C+ l.985iu + i.3667r= -1.558. 
+ 111.671 +7.855 =+3^097- 
+6.071 =+0.099.' 
Solution: M = +0". 139=^0". 002. 

c = — o .169. 
TT = +o".075 ±o".oo7. 
p. e. unit weight =to".oi7. 



B. D. + 42° 1956. 10 Ursae Majoris (8^^ 54™-2, = 42° 11'.) 
Mag. 409. LL = — 0^0388; — o".26i. Spectrum F5. 

The measures are in longitude. This star has a large proper 
motion. Other parallaxes published for it are : 

Flint ( Transits ) — o".oo4 

Belopolsky ( Transits ) +o".020 

Chase (Heliometer) +o".o8 

Adams (Hypothetical) +o".ii 

Table i. 













No. of 




No. of 








Hour 




expo- 


Quality of 


inter- 


No. 




Date 


angle 


Observer 


sures 


images 


polations 








hr. min. 










I 


Nov. 


26, I912 


-0 6 


B. 


3 


2 





2 


Dec. 


9, 1912 


+0 


M. 


3 


2 


I 


3 


Dec. 


13, 1912 





M. 


2 


3 





4 


Dec. 


15. 1912 


-0 24 


B. 


3 


2 





5 


Mar. 


I, 1915 


+0 2 


P. 


2 


3 





6 


Apr. 


I. 1915 





M. 


2 


2 


I 


7 


Apr. 


4, 1915 


5 


P. 


2 


2 





8 


Apr. 


8, 1915 


20 


M. 


2 


2 





9 


Dec. 


30, 1915 


+0 15 


P. 


2 


3 





10 


Jan. 


3. 1916 


15 


S. 


2 


3 





II 


Mar. 


9. 1916 


+0 15 


S. 


3 


3 


I 


12 


Mar. 


II, 1916 


22 


Ma. 


3 


3 


I 



Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(V) 


by 


I 


.7 


-6.76 


+0.848 


+0.026 


.001 


M. 


2 


.6 


6.63 


.710 


.034 


.012 


M. 


3 


•7 


6.59 


.660 


.009 


.Oil 


M. 


4 


.8 


6.57 


.633 


.014 


.006 


M. 


5 


.8 


+ 1-49 


-0.588 


-0.139 


.012 


M. 


6 


.9 


1.80 


.921 


.166 


.003 


M. 


7 


•9 


1-83 


.941 


.157 


.007 


M. 


8 


•7 ^ 


1.87 


.963 


.163 


.002 


M. 


9 


•9 


+4-53 


+0.422 


.184 


.004 


M. 


10 


•9 


4-57 


•357 


.188 


.002 


M. 


II 


•9 


+5-23 


-0.703 


.230 


.008 


M. 


12 


•9 


5-25 


.727 


.234 


.012 


M. 







COMPARISON 


STARS 












Depend- 






Mag- 


No. 


X 


Y 


ence 


Diameter 


B. D. No. 


nitude 


4 


+ 114-235 


+ 100.983 


0.169 


0.41 






5 


— 99.208 


9-905 


0.237 


0.73 


+42° 1953 


9-3 


7 


220.617 


25.200 


0.219 


0.48 


+42° 1952 


9.4 


9 


+ 205.590 


-136.088 


0.375 


0.41 






TT 


24-503 


26.067 


0.54 







Normal equations : 



Solution : 



p. e. unit weight 



9.700C+ 4.811JU— i.4i87r= — 1,213. 
+220.137 -21.767 =-4.985. 
+ 5. 112 =+0.654. 
M=— o".o86 ±0".002. 
c = -o .113. 
7r = +o".o86 ±0".0I5. 
=0".025. 



56 



JOHN A. MILLER 



B. D. +29° 1883. 

jNIag. 7-6 



(9^ 12™. o, + 29° o'.) 

•0".5I2. 



The measures were in longitude. The star is a visual binary 
with a period of 34.00 years. The combined image of the 



components is not sensibly elongated. 

Flint (Transits) found a parallax of 
ometer) found a parallax of o".ooo. 



o".ii9; Chase (HeH- 



Table i. 













No. of 




No. of 








Hour 




expo- 


Quality of 


inter- 


No. 




Date 


angle 


Observer 


sures 


images 


polations 








hr. min. 










I 


Nov. 


29, I9I2 


+ 


Al. 


3 


3 





2 


Dec. 


13, I9I2 


30 


M. 


3 


3 





3 


Dec. 


II, I9I3 


+0 25 


P. 


3 


5 


2 


4 


Dec. 


19. I9I3 


5 


S. 


3 


5 





5 


Apr. 


12, 1914 


+ 1 15 


Al. 


3 


5 





6 


Jan. 


4. 1915 


+0 45 


Al. 


2 


5 





7 


Jan. 


8, 1915 


55 


Al. 


3 


5 





8 


Alar. 


14. I9I5 


+0 40 


Al. 


3 


5 





9 


Alar. 


16, I9I5 


15 


A^l. 


3 


5 





10 


Alar. 


27, I9I5 


I 30 


Ala. 


3 


4 





II 


Apr. 


4. 1915 


34 


p. 


3 


5 





12 


Apr. 


7, 1915 


45 


P. 


3 


5 






Table 2. 





Weight 


Time in 


Parallax 








No. 


of plate 


100 days 


factor 


Solution 


Residual 


Measured 




(P) 


(T) 


(P) 


(m) 


(V) 


by 


I 


.8 


-5-87 


+0.887 


-0.238 


.000 


H. 


2 


.8 


5-73 


.752 


.240 


.000 


H. 


3 


•9 


—2.10 


+0.777 


.193 


.000 


S. 


4 


I.O 


2.02 


.683 


.206 


.012 


H. 


5 


.8 


-0.88 


-0.944 


.194 


.013 


H. 


6 


•7 


+ 1-79 


+0.459 


.141 


.009 


H. 


7 


•9 


1.83 


•395 


.141 


.009 


H. 


8 


1.0 


+2.48 


-0.658 


.168 


.008 


S. 


7 


•9 


2.50 


.684 


.165 


.005 


H. 


10 


•7 


2.61 


.812 


.168 


.008 


S. 


II 


.9 


2.69 


.886 


•159 


.002 


H. 


12 


•9 


2.72 


.908 


•159 


.002 


H. 







COMPARISON 


STARS. 










Depend- 






Mag. 


Xo. 


-Y 


r ; ence 


Diameter 


B. D. Xo. 


nitude 


I 


-283.972 


+ 58.771 0.330 


0.42 


+ 29° 1881 


9.5 


2 


+ 187.830 


— 190.084 0.250 


0.40 






5 


78.080 


+ 88.726 O.19I 


0.38 






6 


18.060 


42.587 ; 0.229 


0.54 


+ 29° 1884 


9.2 


TT 


- 27.891 


- 1.372 


0.48 







Normal equations: 









10.300C+ 0.43 


2fJL- 


0.840: 


-= —I 


.864 








+9747 


2 — 


17-596 


= +0 


.851 










_U 


5-856 


= +0 


028. 


Solution : 






M=+o' 
c= —0 


•059 
180. 


±0" 


004. 










7r= +0' 


.078 


±0" 


015. 




p. e. unit 


wei 


2;ht 


±0".025. 











B.D. +9°2882. 21835(^1111-) (14^18-5, + 8°54'.) 
]\Iag. 5.1 1 — 6.64. u = — o*.oo46; — o".025. Spectrum A. 

The measures were made in longitude. The fainter com- 
ponent of the Struve pair is /?iiii, which is a binary having a 
period of 44.32 years. Xo other determinations have been 
pubHshed. 

Table i. (/Siiii) 



Xo. 



I 
2 
3 
4 
5 
6 

7 
8 

9 
10 

II 
12 



Date 



No. of 
Hour I ! expo- 

angle I Observer | sures 



Feb. 19, 
Feb. 20, 
Mar. 3, 
June 4, 
June 5, 
June 9, 
June 24, 
July 10, 
Feb. 7, 
]Mar. 23, 
June 12, 
June 22, 



i hr. min. 



+ 

o 



I9I5 
I9I5 

I9I5 ; I 

1915 I +0 

1915 1 o 

1915 ! o 



I9I5 
I9I5 

I9I6 
I9I6 
I9I6 
I9I6 



o 
I 

+0 

o 

+0 

I 



20 

25 
20 

10 

15 
26 

36 
30 

35 
18 

25 
25 



M. 

P. 

xMa. 

P. 

Ma. 

P. 

Ma. 

Ma. 

S. 

P. 

P. 

S. 



Quality of 
images 



No. of 

inter- 
polations 



Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(v) 


by 


I 


.9 


-1-93 


+0.844 


+ 0.208 


.002 


S. 


2 


I.O 


1.92 


.835 


.199 


.007 


S. 


3 


•5 


1.81 


.721 


.211 


.005 


S. 


4 


1.0 


-0.88 


-0.704 


.202 


.007 


s. 


5 


.9 


0.87 


•715 


.194 


.001 


s. 


6 


.8 


0.83 


.762 


•193 


.002 


s. 


7 


..8 


0.68 


.906 


.184 


.009 


s. 


8 


•7 


0.52 


-996 


.198 ! 


.006 


s. 


9 


.8 


+ 1.60 


+ 0.932 


.187 1 


.004 


s. 


10 


•7 


2.05 


•435 


.176 1 


.002 


s. 


II 


.8 


+2.86 


— 0.802 


• 163 1 


.006 


s. 


12 


•9 


2.96 


.896 


.170 1 


.003 


s. 



S8 



JOHN A. MILLER 



COMPARISON STARS. (/SlIIl) 









Depend- 






Mag- 


No. 


X 


Y 


ence 


Diameter 


B. D. No. 


nitude 


I 


-142.421 


+ 130.003 


+0.253 


0.56 


+8° 2852 


9.1 


4 


+2II.3I6 


103.157 


•153 


0.34 






7 


103.471 


-177.184 


.274 


0.41 


+9° 2884 


9-3 


lO 


-172.368 


55-975 


.320 


0.34 






TV 


- 30.328 


17.742 




0.49 







Normal equations: 



Solution : 



+9. 800c— 0.130^-1.821- = 4-1.865. 

+30.662 -3.585"= -0.248 

+6.436"= -0.304 



)u=-o".033±o' 
c = +o .191. 

7r=+o".OI3±o" 



.003. 
.007. 



p. e. unit weight ±o".oi7 



Table 



(21835) 











No. of 




No. of 






Hour 




expo- 


Quality of 


mter- 


No. ' 


Date 


angle 


Observer 


sures 


images 


polations 






hr. mill. 










I 


Feb. 19, 1915 


+ 20 


M. 


3 


4 


2 


2 


Feb. 20, 1915 


25 


P. 


3 


5 





3 


Mar. 3, 1915 


I 20 


Ma. 


3 


2 





4 


June 4, 1915 


+ 10 


P. 


3 


5 


I 


5 


June 5, 19 1 5 


15 


Ma. 


3 


4 





6 


June 9, 1915 


26 


P. 


3 


3 





7 


June 24, 1915 


36 


Ma. 


3 


3 





8 


July 10, 1915 


I 30 


Ma. 


2 


3 





9 


Feb. 7, 1916 


+0 35 


S. 


3 


3 


I 


10 


Mar. 23, 1916 


18 


P. 


2 


2 





II 


June 12, 19 1 6 


+0 25 


P. 


2 


3 





12 


June 22, 1916 


I 25 


S. 


3 


3 






Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(v) 


by 


I 


•9 


-1-93 


+ 0.844 


+0.026 


.001 


S. 


2 


I.O 


1.92 


0.835 


.025 


.000 


S. 


3 


•5 


1.81 


0.721 


.026 


.001 


S. 


4 


.7 


-0.88 


-0.704 


.012 


.002 


S. 


5 


•9 


+0.87 


0.715 


.005 


.009 


s. 


6 


.8 


0.83 


0.762 


.017 


.003 


s. 


7 


.8 


0.68 


0.906 


.016 


.003 


s. 


8 


.7 


0.52 


0.996 


.019 


.007 


s. 


9 


.8 


+ 1.60 


+0.932 


.004 


.003 


s. 
s. 


10 


•7 


2.05 


0.435 


— .006 


.003 


II 


.8 


+2.86 


— 0.802 


— .012 


.000 


s. 


12 


•9 


2.96 


0.896 


.013 


.000 


s. 



DETERMINATIOX OF PARALLAXES OF FIFTY STARS 59 



COMPARISON STARS. (111835) 









Depend- 






Mag- 


No. 


X 


y 


ence 


Diameter 


B. D. No. 


nitude 


I 


-142.421 


+ 130.003 


+ 0.255 


0.56 


+8° 2852 


9.1 


4 


+2II.3I6 


103.157 


.156 


0.34 






7 


103.471 


-177.184 


.271 


0.41 


9° 2884 


9.3 


10 


-172.368 


55-975 


.318 


0.34 






TT 


30.124 


16.434 




0.49 







Normal equations: 



Solution: 



p. e. unit weight 



+9. 500c + O.I34M 
30.429 



i.6iOT= +0.091. 
-3.772 =-0.220. 
+6.287 =+0.025. 



M = +o".033: 

C=+0 .010. 
7r= +0".0II ■■ 



=0 .005. 



B. D. + 41° 2076. Bradley 1433. (lo^* i6'n.3, + 41° 44'.) 
Mag. 5.88. ,u = — 0^0109; — o".i50. Spectrum G. 

The measures were made in longitude. Another parallax is 
by Jost. He obtains the value + o".jo. The hypothetical parallax 
computed hy Adams is o".05. 

Taklk I. 











No. of 




No. of 






Hour 




expo- 


Quality of 


inter- 


^ No. 

JL. 


Date 


angle 


Observer 


sures 


images 


polations 


V. 




hr. min. 






1 




Nov. 29, 19 12 


+ 


s. 


2 


' 3 





2 


Dec. 9, 1912 





s. 


3 


2 





3 


Dec. 12, 1912 


-0 6 


B. 


2 


2 





4 


Jan. 14. 1913 


+ 12 


B. 


2 


3 


I 


5 


Apr. 19, 1913 


— 10 


M. 


3 


2 





6 


Apr. 21, 1913 


12 


B. 


2 


2 





7 


Apr. 25. 19 1 3 


24 


B. 


3 


5 


I 


8 


Dec. 4, 1913 


-0 15 


P. 


2 


2 





9 


Dec. 5, 1913 


25 


S. 


2 


5 


I 


10 


Dec. II, 1913 


7 


P. 


3 


5 





II 


Dec. 19, 1913 


20 


s. 


3 


2 





II 


Dec. 30, 1913 


+0 4 


p. 


3 


5 





13 


Jan. 5, 1914 


20 


M. 


3 


2 





14 


Mar. 20, 1914 


-0 30 


p. 


3 


3 





15 


Mar. 22, 1914 


20 


M. 


3 


2 





16 


Apr. 12, 1914 


+0 15 


M. 


3 


5 





17 


Apr. 17, 1914 


15 


P. 


3 


5 





18 


Apr. 18, 1914 


— 10 


S. 


I 


3 





19 


Apr. 23, 1914 


+ 20 


AI. 


2 


5 





20 


May 2. 19 14 


17 


M. 


3 


5 






6o 



JOHN A. MILLER 



Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(V) 


by 


I 


.8 


-2.75 


+ 0.939 


— 2.164 


.008 


S. 


2 


.9 


2.65 


.870 


2.163 


.006 


S. 


3 


•7 


2.62 


.844 


2. 171 


.013 


S. 


4 


•7 


2.29 


.422 


2.165 


.000 


M. 


5 


7 


-1-34 


- .940 


2.177 


.012 


M. 


6 


.7 


1.32 


.952 


2.182 


.007 


M. 


7 


•7 


1.28 


.973 


2.186 


.004 


M. 


8 


.8 


+0.94 


+ 0.909 


2.160 


.001 


S. 


9 


.8 


0-95 


.902 


2.156 


.004 


s. 


10 


•7 


I.OI 


•855 


2.155 


.005 


M. 


II 


•9 


1.09 


•777 


2.158 


.004 


M. 


12 


•9 


1.20 


•644 


2.153 


.Oil 


S. 


13 


I.O 


1.26 


.561 


2.165 


.000 


S. 


14 


•7 


+2.00 


- .636 


2.200 


.014 


Mt. 


15 


•4 


2.02 


.662 


2.202 


.016 


M. 


16 


•5 


2.23 


.888 


2.192 


.001 


M. 


17 


1.0 


2.28 


.926 


2. 191 


.001 


S. 


18 


.2 


2.29 


.932 


2.195 


.003 


S. 


19 


.7 


2.34 


.962 


2.200 


.008 


S. 


20 


.7 


2-43 


.998 


2-199 


.006 


M. 



COMPARISON STARS. 



No. 


X 


Y 


Depend- 
ence 


Diameter 


B. D. No. 


Mag- 
nitude 


2 

3 

TT 


+260.046 
-I66.I3I 

93-915 
+ 44-560 


-113.604 

+ 102.409 

II. 195 

- 59-227 


+0.33 

-0-33 
+ 1.00 


0.68 

0.66 
0.47 
0.41 


+41° 2078 
41° 2072 
41° 2073 


8.7 

8.0 
8.5 



Normal equations : 



Solution 



51.720/X+ 4.156c— 7. 8207r= — 9.209. 

+ 14.508+ 0.662 =-31-537. 

+ 10.209 =- 1-259- 



p. e. unit weight ±o".022. 



M=-o".oo3 +o".oo3. 

C=-2 .174. 

7r=+o".o8o ±0^.007. 



B. D. + 56° 1459. 36 Ursse Majoris. {id^ 24'^.2, + 56° 30'.) 
Mag. 4.84. jx = — 0^0215; — o".038. Spectrum F. 

The measures were made in longitude. This star has large 
proper motion. The field of the comparison stars by which the 
parallax was computed was chosen by the method described on 
page 10. The field chosen in this way consisted of stars numbered 
2, 4, 5, and 7. Before the measures were made to determine the 



DETERMINATION OF PARALLAXES OF FIFTY STARS 6i 

final field, I chose in the usual way a field which consisted of 
stars numbered 4, 5, 6, and 7. Both fields were measured at the 
same time and a parallax found from each of them. Observa- 
tional data are given in Table i. The reduction for the field 2, 
4, 5, and 7 is given in Table 2, which is followed by the normal 
equations and the solution for this field. Table 3 gives the 
reduction for the field 4, 5, 6, and 7. Following Table 3 are 
the normal equations and the solution for this second field. 
No other parallax of this star has been published. 

Table i. 











No. of 




No. of 






Hour 




expo- 


Quality of 


inter- 


No. 


Date 


angle 


Observer 


sures 


images 


polations 






hr. min. 










I 


Apr. 4, 1915 


+0 25 


P. 


2 


4 





2 


Apr. 6, 1915 


20 


M. 


2 


4 





3 


Apr. 15, 1915 


20 


M. 


3 


3 





4 


Nov. 29, 1915 


— 20 


S. 


I 


3 





5 


Dec. 4, 1915 


20 


M. 


2 


3 





6 


Dec. 10, 1915 


6 


Ma. 


2 


2 





7 


Dec. 22, 1915 


50 


M. 


I 


2 





8 


Dec. 23, 1915 


+ 


P. 


I 


2 





9 


Jan. 8, 1916 


20 


M. 


2 


3 





10 


Mar. 31, 1916 


-0 3 


P. 


3 


3 





II 


Apr. 18, 1916 


+ 20 


M. 


3 


2 





12 


Apr. 29, 1916 


28 


Ma. 


2 


2 






Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(v) 


by 


I 


.8 


-2.24 


-0.873 


— 0.120 


.002 


M. 


2 


.8 


2.22 


.890 


.130 


.007 


M. 


3 


.8 


2.13 


•952 


.120 


.004 


M. 


4 


.7 


+ 0.15 


+0.902 


.091 


.001 


M. 


5 


.9 


0.20 


.863 


.088 


.004 


M. 


6 


.7 


0.26 


.807 


•095 


.002 


M. 


7 


.6 


0.38 


.668 


.080 


.016 


M. 


8 


.6 


0.39 


.655 


.103 


.006 


M. 


9 


.8 


0.55 


.424 


.118 


.015 


M. 


10 


.8 


+ 1.38 


-0.844 


.121 


.012 


M. 


II 


.8 


1.56 


.972 


.132 


.004 


M. 


12 


•7 


1.67 


1.004 


.152 


.015 


M. 



62 



JOHN A. MILLER 



COMPARISON STARS. 









Depend- 


i 


Mag- 


No. 


X 


Y 


ence 


Diameter ; B. D. No. 


nitude 


2 


— 108.617 


+ 223.714 


+0.405 


0.36 




4 


119-335 


-222.742 


0.270 


0.32 






5 


+ 78.227 


147-303 


0.143 


0.29 






7 


149.724 


+ 146.332 


0.182 


0.40 






TT 


- 37-922 


36.138 




0.77 







Normal equations: 



Solution 



p. e. unit weight 



9.000c— 0.382/^-1.222-= —1. 019. 

+ 17.528 +2.338 =+0.037. 
+6.365 =+0.267. 



'028. 



M=-0 .015 

c= —o .110. 

7r=+0".I03 



.007. 
,012. 



Table 3. 



No. 



I 
2 

3 

4 
5 
6 

7 
8 

9 

10 
II 

12 



Weight Time in 






Resid- 




of plate 100 days 


Parallax factor 


Solution 


ual 




(p) (T) 


(P) 


(m) 


(V) 


Measured bi' 


Same as Table 2 


Same as Table 2 


+0.044 


.002 


Same as Table 2 


Same as Table 2 


Same as Table 2 


.026 


.016 


Same as Table 2 


Same as Table 2 


Same as Table 2 


.055 


.014 


Same as Table 2 


Same as Table 2 


Same as Table 2 


-075 


.001 


Same as Table 2 


Same as Table 2 


Same as Table 2 


.072 


.002 


Same as Table 2 


Same as Table 2 


Same as Table 2 


.067 


.006 


Same as Table 2 


Same as Table 2 


Same as Table 2 


.087 


.017 


Same as Table 2 


Same as Table 2 


Same as Table 2 


.070 


.000 


Same as Table 2 


Same as Table 2 


Same as Table 2 


•055 


.009 


Same as Table 2 


Same as Table 2 


Same as Table 2 


.052 


.012 


Same as Table 2 


Same as Table 2 


Same as Table 2 


.036 


.001 


Same as Table 2 


Same as Table 2 


Same as Table 2 


.025 


.Oil 


Same as Table2 



COMPARISOX STARS. 



No. 


X 


Y 


Depend- 
ence 


Diameter B. D. No. 


Mag- 
nitude 


4 

5 
6 

7 


— 111.901 
+ 85.661 
-130.917 

+ 157.158 
- 30.488 


-225.893 
150.454 

+233-165 

143-I81 

32.987 


+0.254 
0.170 
0.372 
0.204 


0.32 1 

0.29 

0.42 

0.40 

0.77 





Normal solutions : 



Solution: 



S.gooc — o.402ju — 1 .309- = 0.485. 

17.524M+2.321 =0.005. 

6.290 =0.044. 



p. e. unit weight ±o".030. 



— o 
+ 
+0" 



.004=^0 .007. 

057- 
.090=^0". 013. 



DETERMINATION OF PARALLAXES OF FIFTY STARS 6z 

B.D. + 36°2i47. Lalande2ii85. (loi^ 57'°.9, + 36° 38'.) 
Mag. 7.8. H- = — 0^.0469; — 4 ".746. 

The measures are in longitude. This star has a large proper 
motion. Kapteyn computed an absolute parallax from the 
measures of Winnecke, Kapteyn, Flint, Jost, Russell, and Chase 
to be + o''.403. The smallest parallax given by the authorities 
cited is that of Russell, whose value is + o".35o, and the largest 
that derived by Winnecke, which is + o".507. 

Table i. 



No. 


Date 


Hour 
angle 


Observer 


No. of 
expo- 
siires 


Quality of 
images 


I 
2 
3 


Apr. 25, 1912 
Apr. 27, 1912 
May 4, 19 12 


hr. min. 

+0 

24 

12 


M. 
B. 
B. 


2 

2 
3 


I 

3 

I 


4 


Dec. 9, 1912 


+ 


AI. 


2 


5-1 


5 
6 

7 
8 


Apr. 19, 1913 
Apr. 21, 1913 
Apr. 25, 1913 
May 8, 19 13 


+ 
12 

-0 24 

+ 


M. 
B. 
B. 

M. 


3 

I 

2 


2 

5 
4 
5 


9 
10 
II 
12 

13 
14 


Dec. 4, 1913 
Dec. 5, 1913 
Dec. II, 1913 
Dec. 19, 1913 
Dec. 30, 1913 
Jan. 5, 1914 


+ 

— 10 

+0 3 

— 20 

+0 29 

20 


P. 
S. 
P. 

s. 
p. 

M. 


3 

3 
3 
3 
3 

1 2 


4 
5 
4 
5 
4 
3 



No. of 

inter- 
polations 



Table 2. 



■ 


Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(v) 


by 


I 


•7 


-2.51 


— 0.910 


+2.225 


• Oil 


s. 


2 


.7 


2.49 


.924 


2.2II 


.003 


s. 


3 


•7 


2.42 


.964 


2.215 


.001 


s. 


4 


.6 


-0.23 


+0.941 


2.519 


.003 


s. 


5 


•9 


+ 1.08 


-0.857 


2.440 


.005 


s. 


6 


.9 


1. 10 


.875 


2.435 


.001 


s. 


7 


.8 


1. 14 


.907 


2.422 


.012 


s. 


8 


•7 


1.27 


.984 


2.442 


.007 


s. 


9 


•9 


+3.37 


+0.964 


2.744 


.003 


§• 


10 


•9 


3.38 


.960 


2.745 


.003 


s. 


II 


•9 


3-44 


•931 


2.755 


.012 


s. 


12 


I.O 


3-52 


.876 


2.739 


.003 


s. 


13 


.9 


3-63 


■772 


2.735 


.004 


s. 


14 


.8 


3-69 


.703 


2.732 


.005 


s. 



64 



JOHN A. MILLER 



COMPARISON STARS. 









Depend- 






Mag- 


No. 


X 


Y 


ence 


Diameter 


B. D. No. 


nitude 


I 


-122.499 


-151-717 


0.23 


0.78 


+37°2I5I 


7-7 


2 


141. 130 


84-550 


0.22 


0.51 


37° 2149 


9.3 


3 


96.488 


+251-938 


0.19 


0.48 






7 


+ 360.115 


- 15.671 


0.36 


i 0.58 






TT 


54.532 


11.908 




1 0.54 







Normal equations: 



Solution: 



p. e. unit weight 



83. 522M + 17.343C + 17. 734- =49.154. 

+ 11.409 + 0.333 =29,020. 

+ 9-197 = 2.735. 



M" 


= +0' 


'.283 ±0' 


'.004. 


c = 


= +2 


.449. 




7t- 


= +0' 


'-443^0' 


'.010. 



B. D. + 61° 1246. OS 235. (11^^ 26™.7, +61° 38'.) 
Mag. 5.47. ," = — 0^0005; — o".079. Spectrum F. 

The measures are in right ascension. This is a binary star 
with a period of 71.9 years. The components are sufficiently 
near the same magnitude and close enough together so that the 
combined image of the components is not sensibly elongated. 

Russell finds a hypothetical parallax of o",032. 

Table i. 



No. 




Date 


Hour 
angle 


Observer 


No. of 
expo- 
sures 


Quality of 
images 


No. of 
inter- 
polations 


I 
2 


Feb. 
Feb. 


1, I914 

2, I9I4 


hr. mill. 
+ 

-0 6 


P. 

M. 


3 
3 


4 
2 






3 


May 


2, I914 


-0 5 


M. 


3 


I 





4 
5 
6 

7 


Jan. 
Jan. 
Jan. 
Feb. 


4. 1915 

14. I915 
29. I915 
18, I915 


+0 10 
-0 15 
+0 15 

28 


M. 
M. 
M. 
P. 


3 
2 

3 
3 


2 
3 

4 


I 






8 

9 
10 
II 
12 


Apr. 
Apr. 
Apr. 
Apr. 
Apr. 


6, 1915 

7, 1915 
15. 1815 

17. 1915 

18, 1915 


-0 5 

47 

+0 20 

15 
— 20 


M. 

P. 

M. 

Ma. 

M. 


I 

2 

I 


3 
5 
4 
4 
4 










DETERMIXATION OF PARALLAXES OF FIFTY STARS 65 



Table 2, 





Weight 


Time m 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(V) 


by 


I 


•9 


-3-08 


+ 0.56 


+0.155 


.002 


S. 


2 


.8 


3-07 


•55 


.160 


.003 


S. 


3 


.8 


-2.18 


-0.72 


.148 


.001 


s. 


4 


.8 


+0.29 


+0.83 


.167 


.008 


s. 


5 


.6 


0.39 


.76 


.189 


.014 


s. 


6 


.8 


0.54 


.61 


.170 


.004 


S. 


7 


•9 


0.74 


•2>2 


.174 


.003 


S. 


8 


•9 


+ 1.21 


-0.39 


.164 


.002 


S. 


9 


I.O 


1.22 


.40 


•159 


.007 


S. 


10 


I.O 


1.30 


•53 


•163 


.002 


S. 


II 


.8 


1.32 


•54 


•179 


.014 


s. 


12 


I.O 


1-33 


•55 


•163 


.002 


s. 



COMPARISON STARS. 









Depend- 






Mag- 


Xo. 


X 


r 


ence 


Diameter 


B. D. No. 


nitude 


2 


-1 13.92 1 


-201.247 


0.479 


0.30 


+61° 1248 


9.4 


3 


+ 12.835 


+207.606 


0.275 


0.39 


62 II86 


9^5 


4 


71.386 


206.555 


0.129 


0.41 


62 1 187 


9.4 


5 


29.700 


-212.914 


O.II7 


0.36 






■7V 


- 38.426 


37.820 




0.60 







Normal equations: 



Solution: 



p. e. unit weight ±o".022 



IO.30OC+ 0.587/x + O.OOITr = 1.702. 

+28.423 -3^704 =0.182. 

+3.340 =0.020. 

o".oo4. 

o".oi3. 



M = +o' 
c= +0 

7r= +0' 



.021 

•165. 

.051 



B. D. + 15° 2383. ;3 Leonis = ,3 604. (iiM4'"^o. + 15° 8'.) 
Mag. 2.23. u = — o^0342; — o".i23. Spectrum A2. 

The measures were made in longitude. The quahty of these 
plates was not good, and the magnitude of the comparison stars 
unequal. Parallaxes of this star published by Pritchard, Chase, 
and Flint are as follows : 

Pritchard ( Photography) 0^.0490 

Chase (Heliometer) o".i2 

Flint (Transits) o".03i 



66 



JOHN A. MILLER 



Table i. 















No. of 




No. of 










Hour 




expo- 


Quality of 


inter- 


No. 


Date 




angle 


Observer 


sures 


images 


polations 










hr. mill. 










I 


May 


4. 


1912 


+ 1 6 


B. 


3 


2 


I 


2 


May 


19. 


1912 


30 


B. 


3 


3 


I 


3 


Jan. 


14, 


1913 


-0 24 


B. 


3 


4 





4 


Feb. 


7) 


1913 


+0 30 


M. 


2 


2 





5 


Feb. 


13, 


1913 


24 


B. 


3 


3 


I 


6 


Feb. 


14, 


1913 


I 


M. 


3 


3 





7 


Apr. 


25, 


1913 


-0 24 


B, 


3 


4 


I 


8 


May 


14, 


1913 


12 


B. 


3 


5 





9 


May 


19, 


1913 


+0 18 1 


B. 


3 


5 


I 


10 


Dec. 


II, 


1913 


+0 7 


P. 


2 


3 


2 


II 


Jan. 


5, 


1914 


20 


M. 


3 


3 


2 


12 


Feb. 


I, 


1914 


38 


P. 


3 


5 


I 


13 


Feb. 


2, 


1914 


I 


M. 


2 


3 





14 


Apr. 


17, 


1914 


+0 30 


P. 


3 


5 





15 


Apr. 


30, 


1914 


20 


M. 


3 


4 





i6 


Mav 


14, 


1914 


20 


M. 


3 


3 


I 



Table 





Weight 


Time in 


Parallax 










of plate 


100 davs 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(v) 


by 


I 


•7 


-3.62 


-0.809 


-2.493 


.017 


S. 


2 


I.O 


3-47 


.940 


2.514 


.003 


s. 


3 


•7 


— 1.07 


+ 0.813 


2.556 


.017 


M. 


4 


.6 


0.83 


•514 


2.564 


.Oil 


M. 


5 


•7 


•77 


•415 


2.553 


.014 


M. 


6 


•7 


.76 


•399 


2.552 


.015 


M. 


7 


•9 


—0.06 


— 0.711 


2.621 


.017 


M. 


8 


•9 


+0.13 


•905 


2.625 


.Oil 


M. 


9 


•7 


.18 


.942 


2.617 


.001 


M. 


10 


.8 


+2.24 


+0.984 


2.632 


.007 


M. 


II 


•7 


2.54 


.893 


2.631 


.004 


M. 


12 


.8 


2.76 


.604 


2.642 


.006 


M. 


13 


.7 


2.77 


•590 


2.630 


.018 


M. 


14 


•9 


+3.51 


— 0.602 


2.690 


.008 


S. 


15 


•9 


3-64 


.766 


2.713 


.008 


S. 


16 


•7 


3.78 


.901 


2.710 


.002 


M. 



DETERMINATION OF PAR ALE AXES OF FIFTY STARS 67 



COMPARISOX STARS. 









Depend- 






Mag- 


No. 


X 


Y 


ence 


Diameter 


B. D. No. 


nitude 


I 


-183755 


- 54-730 


0.26 


0.42 






2 


46.221 


+ 116.326 


0.14 


0.56 






3 


3-133 


42.816 


0.17 


0.83 


+ 15° 2822 


8.2 


4 


+ 97-569 


- 65.944 


0.23 


0.59 






5 


135-542 


38.470 


0.20 


0.40 






IT 


- 2.639 


13.468 




0.61 







Normal equations: 



Solution; 



76. 



p. e. unit weight ="=0' 



326M+ 8.666c 

+ 12. 411 -I 

+7 

M= — 0".I27=fc 
C=-2 .588. 
7r=+0".Il6=t 

035- 



+2.855- = +24.415. 
731 =+32.391. 
,301 =- 4.582. 

o".oo4. 
o".oi3. 



B. D. + 11° 2589. Lalande 25224 — ,3 612. 

Mag. 5.54. fj. = —0^0076; — o".oii. Spectrum A. 

The measures are made in longitude. This is a binary star 
with a period of 23.05 years. The components are of the same 
magnitude and so close that their combined image, if at all long, 
is very slightly so. The combined image was bisected in making 
the measurements. 

Flint published a parallax of + o".25 and Russell a hypo- 
thetical parallax of o".o2i. 

Table i. 



No. 


Date 


Hour 
angle 


Observer 


No. of 
expo- 
sures 


Quality of 
images 


No. of 
inter- 
polations 


I 


June 9, 1912 


hr. mill. 
+ 18 


B. 


3 


I 





2 

3 


Feb. 14, 1913 
Mar. II, 19 13 


+ 40 

54 


I': 


3 
3 


2 
2 


2 



4 

5 
6 


May 8, 1913 
May 19, 1913 
June 12, 1913 


+0 
— 12 

+ 1 


M. 
B. 

M. 


3 
2 

3 


5 
4 
4 


2 
2 

4 


7 
8 

9 
10 


Feb. I, 1914 
Feb. 7, 19 14 
Mar. 3, 1914 
Mar. 4, 19 14 


+0 25 

-0 3 

22 

+0 4 


P. 

S. 
P. 

s. 


3 
3 
3 
2 


5 
4 
5 
4 


I 
I 




II 
12 


May 18, 1914 
May 31, 19 14 


+0 15 
50 


s. 

M. 


3 

3 


3 

5 


2 




68 



JOHN A. MILLER 



Table 2. 



No. 


Weight 
of plate 


'lime m 

100 days 

(T) 


Parallax 

factor 

(P) 


Solution 
(m) 


Residual 

(V) 


1 Measured 

1 by 


I 


.7 


-4-79 


-0.889 


-1.266 


.010 


s. 


2 

3 


.7 
•9 


-2.29 
2.04 


+ 0.774 

-444 


1.256 

1-259 


.009 
.005 


1 s. 
1 s. 


4 
5 
6 


.8 

•7 
.8 


-1.46 

1-35 
I. II 


-0.508 
.661 
.911 


1.250 
1.266 
1.262 


.Oil 

.005 

.002 


s. 
s. 

! S. 

1 


7 
8 

9 
10 


.9 
.9 
•9 

.8 


+ 1.23 
1.29 

1-53 
1.54 


+0.893 
-845 
.566 

•552 


1.260 
1.273 
1.279 
1.277 


.008 
.005 
.012 
.010 


s. 
s. 
s. 
s. 


II 
12 


•5 
.9 


+2.29 

2.A2 


-0.645 

.802 


1.262 
1.256 


.002 
.007 


i: 



COMPARISON STARS. 









Depend- 






Mag- 


No. 


X 


F 


ence 


Diameter 


B. D. Xo. 


nitude 


I 


+ 55-569 


- 74-098 


0.07 


0.45 






2 


139-937 


27.679 


0.16 


0.40 






3 


127.167 


+ 42.080 


0.33 


0.48 


+ 11° 2590 


9.2 


4 


-322.674 


59.696 


0.44 


0.49 


+ 11 2584 


9-3 


TT 


75.011 


30.302 




0.67 







Normal equations: 



Solution: 



42.220M-i.595c+3-8937r=+ 1.962. 

+9.505 +0.194 =-12.010. 

+5.004 = — 0.266. 



p. e. unit weight =i=o".026. 



/i= — o".oo5±o."oo4. 

c= — I .264. 

x= — o".oi6=to".oi2. 



B.D. +42°253i. 



OS 285. 
Mag. 7.1 - 



(i4Mi"-7, +42°49'-) 
7.6. 

The measures were in right ascension. This is a close binary 
star with a long period. The components are of about the same 
magnitude and so close together that the combined image shows 
no elongation. The image was bisected in making the measures. 

Russell determined a hypothetical parallax of o" .012 for 
this star. 



DETERMIXATION OF PARALLAXES OF FIFTY STARS 6g 



Table i. 



Xo. 



Date 



Hour 
angle 



Obse 



Xo. o 
expo- 



Quality of 
images 



Xo. of 
inter- 
polations 











hr. 


nin. 




I 

2 

3 
4 


Mar. 
Alar. 
Mar. 
Mar. 


3. 
4- 

12, 

24, 


1914 
1914 
1914 
1914 


— 





30 
16 
36 

5 


P. 
s. 
p. 


5 
6 


Mar. 
Apr. 


25' 

4- 


1915 
1915 


+ 



36 


P. 
P. 


7 
8 

9 


June 
June 
June 


17. 
20, 

28. 


1915 
1915 
1915 


+ 




20 1 
20 
20 i 


M 
M 
M 


10 

II 


June 
June 


22, 
26, 


1916 
1916 


+ 



30 
17 


S. 
P. 


12 


June 


30. 


1916 





20 


P. 



Table 2. 





VVeignt 


iime in 


Jr'arailax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


Xo. 


(P) 


(T) 


(P) 


(m) 


(V) 


by 


I 


.9 


-3-98 


+0.82 


— 0.040 


.004 


S. 


2 


.8 


3-97 


.81 


.034 


.002 


S. 


3 


.8 


3-89 


•73 


.035 


.000 


S. 


4 


I.O 


3-77 


•59 


.035 


.001 


S. 


5 


•9 


— O.II 


+0.58 


.059 


.000 


S. 


6 


.8 


O.OI 


•45 


•059 


.000 


s. 


7 


.8 


+0.73 


-0.66 


.052 


.005 


s. 


8 


.8 


0.76 


.69 


.050 


.007 


s. 


9 


•5 


0.84 


•77 


•073 


.017 


s. 


10 


.6 


4-44 


-0.73 


.077 


.003 


s. 


II 


.8 


4.48 


•77 


.082 


.003 


s. 


12 


.~ 


4-52 


.81 


.081 


.001 


s. 



COMPARISON STARS. 









Depend- 






Mag- 


Xo. 


X 


r 


ence 


Diameter 


B. D. Xo. 


nitude 


I 


+202.520 


+ 11.649 


+0.041 


0.57 


+ 42° 2533 


9.2 


2 


126.968 


-77-278 


0.414 


0.37 






3 


— 129.184 


+23.131 


0.277 


0.38 


42 2529 


9.5 


4 


200.305 


42.497 


0.268 


0.47 


42 2527 


9^5 


IT 


28.6^8 


— T^.-=-' 




O.i.2 







Normal equations : 



Solution : 



p. e. unit weight =t:o".oi6. 



9.400^- 2.723M+ 0.35677= -0.514. 
96.622(5-18.462 =—0.348. 
4.648 =+0.069. 
M= — o".03o±o".0O3, 
c= —o .056. 

7r= — 0".028±0".0I5. 



70 



JOHN A. MILLER 



B.D. + 37° 2636. //Bootis. (15^ 23^.7; + 37° 44'-) 
Mag. 447. ," = — 0^0126; -f o".078. Spectrum F. 



This star is measured in longitude, 
star has been published. 

Table i. 



No parallax for this 













No. of 




No. of 








Hour 




-expo- 


Quality of 


inter- 


No. 


Date 




angle 


Observer 


sures 


images 


polations 








hr. milt. 










I 


Mar. 17, 


1913 


+0 30 


M. 


3 


3 





2 


June 30, 


1913 


-0 36 


B. 


3 


4 





3 


July 4. 


1913 


6 


B. 


3 


3 





4 


Feb. 7, 


1914 


+0 20 


S. 


3 


2 


I 


5 


Mar. 4, 


1914 


13 


s. 


2 


4 





6 


Mar. 13, 


1914 


25 


M. 


2 


2 





7 


Mar. 20, 


1914 


— 10 


M. 


3 


2 





8 


Mar. 24, 


1914 


7 


M. 


3 


4 





9 


Mar. 12, 


1915 


+0 30 


M. 


2 


2 





10 


Mar. 31, 


1915 


-0 15 


Ma. 


3 


4 


I 


II 


June 5, 


1915 


+0 10 


Ma. 


3 


5 





12 


June 9, 


1915 


-0 25 


P. 


3 


3 





13 


, une 28, 


1915 


+0 30 


M. 


3 


5 





14 


July I , 


1915 


23 


Ma. 


3 


5 






Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(v) 


by 


I 


•5 


-4.83 


+0.572 


+0.047 


.006 


P. 


2 


.6 


-3-78 


-0.937 


.029 


.Oil 


P. 


3 


•5 


3-74 


.961 


— 0.012 


.029 


P. 


4 


.9 


-1.56 


+0.945 


+0.008 


.003 


P. 


5 


•9 


I-3I 


.740 


.004 


.004 


P. 


6 


•5 


1.22 


1.629 


.007 


.009 


P. 


7 


•9 


I-I5 


•532 


— 0.008 


.006 


P. 


8 


•7 


I. II 


.472 


.000 


.004 


P. 


9 


•9 


+2.42 


+0.646 


0.059 


.014 


P. 


10 


I.O 


2.61 


•369 


.052 


.004 


P. 


II 


■5 


+3-27 


— 0.691 


+0.051 


.013 


P. 


12 


■9 


3-31 


•738 


.060 


.004 


P. 


13 


8 


3-5':» 


.921 


.069 


.002 


P. 


14 


1.0 


3-53 


.941 


.065 


.004 


P. 



DETERMINATION OF PARALLAXES OF FIFTY STARS 71 



COMPARISON STARS. 



No. 


-^ 


Y 


Depend- 
ence 


Diameter 


B. D. No. 


Magni- 
tude 


2 
3 

5 


+ 139-266 
-176.234 

+ 36.969 
— 20.296 


- 65.035 
96.530 

+ 161.566 
21.686 


0.201 

0.365 
0.434 


0.83 
0.67 
0.64 
1.20 


+37° 2639 
38° 2654 


8.9 
9.2 



Normal equations: 

10.600C+ 4.i74/z+o.i467r= — 0.262. 

+ 83.311 -7.821 =-I.I2I. 

+5.863 =+0.130. 
Solution: yu = — o".055 ±o".oo3. 

c= —o .020. 

7r=+0".033±0".0I3. 
p. e. unit weight ±o".029. 



B. D. + 37° 2637. 1^' Bootis = 2 1938. (15' 20-7, + 37° 44') 
Mag. 6.66. // = — o*.oi22; + o".093. Spectrum K. 

The measures are in longitude, i^- Bootis is a binary with a 
very uncertain period. The combined image of the two com- 
ponents is elongated, but the images are never separated on the 
plates. In the measurements the attempt was made to bisect 
this elongated image. The components are so nearly of the 
same magnitude that the image is fairly symmetrical though 
long. 

Flint found for the parallax of this star the value of + o".oi9. 
Russell's hypothetical parallax is + o".033. 

Table i. 



No. 


Date 


Hotir 
angle 


Observer 


No. of 
expo- 
sures 


Quality of 
images 


No. of 
inter- 
polations 


I 


Mar. 17, 1913 


kr. mill. 

+0 30 


M. 


3 


3 





2 

3 


June 30, 1913 
July 4, 19 13 


-0 36 

6 


B. 
B. 


3 
3 


4 
3 






4 
5 
6 

I 


Feb. 7, 1914 
Mar. 4, 1914 
Mar. 13, 1914 
Mar. 20, 1914 
Mar. 24, 1914 


+ 20 

13 
25 

— 10 

7 


S. 

S. 

M. 

M, 

M. 


3 
2 
2 

\ 


2 

4 
2 
2 

4 


I 







9 
10 


Mar. 12, 1915 
Mar. 31, 1915 


+0 30 
-0 15 


M. 
Ma. 


2 

3 


2 
4 




I 


II 
12 

13 
14 


June 5, 1915 
June 9, 1915 
June 28, 1915 

July I, 1915 


+0 10 

-0 23 

+0 30 

23 


Ma. 
P. 

M. 
M. 


3 
3 
3 
3 


5 
3 
5 
5 











72 



JOHN A. MILLER 



Table 2. 





Weight 


Tinae in 


Parallax 










of plate 


100 davs 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(v) 


by 


I 


.8 


-4.83 


+ 0.572 


+ 0.071 


.014 


P. 


2 


•5 


-3-78 


-0.937 


.033 


•003 


P. 


3 


•5 


3-74 


.961 


.013 


.016 


P. 


4 


.6 


-1.56 


+0.945 


.025 


.007 


P. 


5 


I.O 


1-31 


.740 


•033 


.005 


P. 


6 


•9 


1.22 


.629 


• .018 


.007 


P. 


7 


•9 


1. 15 


•532 


.026 


.003 


P. 


8 


1.0 


I. II 


•472 


.013 


.009 


P. 


9 


•7 


+2.42 


+0.646 


-0.013 


.005 


P. 


10 


1.0 


2.61 


.369 


.006 


.006 


P. 


II 


.5 


+3.27 


— 0.691 


.019 


.Oil 


P. 


12 


.8 


3-31 


.738 


.036 


.004 


P. 


13 


.8 


3.50 


.921 


•035 


.000 


P. 


14 


1.0 


3-53 


.941 


.032 


.003 


P. 



COMPARISON STARS. 



No. 


X 


Y 


Depend- 
ence 


Diameter 


B. D. Xo. 


Magni- 
tude 




+ 139.266 
-176.234 
+ 36.969 
— 11.064 


- 65.035 

96.530 

+ 161.566 

0.721 


0.293 
0.366 
0.341 


0.83 
0.67 
0.64 
0.72 


+ 37^2639 
38° 2654 


8.9 
9.2 



Normal equations: 



Solution: 



ii.ooO(:+ i.8o4ju+o.5397r= +0.067. 

+ 87.022 —9.189 =—0.869. 

T-5-757 =+0.152. 



p. e. unit weight ±0". 024. 



M= — o ,042 —0 .003. 

c = +0 .007. 

x= +o".054 — o".oii. 



B. D. + 26= 2722. }' Coronas Borealis - 2 1967. (15*^ 38^.6, + 26° 37'.) 
yiag. 3.93. ,"= — o^oo75; + o".030. Spectrum A. 

The measures are in longitude. This is a binary with a period 
of 73 years. The combined image of the components was not 
sensibly elongated and was bisected in measuring. 

Russell finds a parallax (h3-pothetical) of + ©".025 for this 
star. 



DETERMINATION OF PARALLAXES OF FIFTY STARS 73 



Table i, 







i 




No. of 




No. of 






Hour ' 




expo- 


Quality of 


inter- 


No. 


Date 


angle 


Observer 


sures 


images 


polations 






hf. min. 










I 


July 5- 19 1 2 


+ 12 


B. 


3 


I 





2 


July II, 1912 


I 15 


M. 


2 


5 





3 


Mar. 2, 1913 


+ 


B. 


2 


I 





4 


Mar. II, 1913 


30 


B. 


3 


3 





5 


Mar. 4, 19 14 


+0 43 


S. 


3 


2 


2 


6 


Mar. 13, 1914 


I 10 


M. 


3 


3 





7 


Mar. 20, 19 14 





M. 


3 


5 





8 


Mar. 24, 1914 


50 


M. 


3 


5 





9 


Apr. 5, 1914 


50 


P. 


3 


5 


I 


10 


June 2S, 1915 


+0 45 


M. 


2 


4 





II 


July 6, 19 1 5 


30 


M. 


3 


5 





12 


July 8, 1915 


I 10 


Ma. 


3 


5 






Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(V) 


by 


I 


■7 


-5.74 


-0.880 


-0.837 


.004 


S. 


2 


.7 


5.68 


.926 


.842 


.002 


s. 


3 


•7 


-3-34 


+ .871 


.813 


.004 


s. 


4 


.8 


3-25 


.788 


.810 


.001 


s. 


5 


.8 


+0.33 


+ .856 


.775 


.003 


s. 


6 


.8 


.42 


.769 


.771 


.008 


s. 


7 


.9 


.49 


.689 


•774 


.004 


s. 


8 


I.O 


.53 


.638 


.782 


.003 


s. 


9 


•9 


•65 


.470 


.784 


.005 


s. 


10 


.6 


+5-14 


-0.806 


•749 


.000 


s. 


II 


.8 


5.22 


.881 


•747 


.003 


s. 


12 


.8 


5.24 


.898 


•753 


.003 


s. 







COMPARISON 


STARS. 












Depend- 






Magni- 


No. 


.Y 


F 


ence 


Diameter ; 


B. D. No. 


tude 


2 


— 40.819 


+ 2.047 


0.20 


0.38 






4 


+ 118. 117 


148.604 


0.22 


0.66 






5 


164.084 


-169.952 


0.21 


0.68 






6 


-136.999 


+ 208.004 


0.19 


0.28 


+2.6° 2720 


8.9 


7 


104.384 


-188.703 


0.18 


0.37 


2.6 2721 


9.1 


TT 


+ 6.649 


+ 2.926 1 


0.39 







Normal equations : 



Solution : 



9.50OC+ o.675/i+i.o527r= -7.466. 

+ 122.631 -5.396 =+0.451. 

+5.918 =-0.834. 

/x = +0". 039 ±0". 001. 



p. e. unit weight ±0". 013. 



c= —0 

7r=+0' 



, / o / . 
.031 



o".oo6. 



74 JOHN A. MILLER 

B. D. + 31° 2884. C Herculis = 2 2084. (16'' 37^^.5, +31° 47'.) 
Mag. 3.00. fi= — o\ 0365; + o". 385. Spectrum G. 

The measures are in longitude. This is a binary with a 
period of 34.53 years. The combined image of the two com- 
ponents is shghtly elongated. It was bisected in measuring. 
Parallaxes by Russell, Flint, and Smith are as follows : 

Russell (Photography) +o".ioi 

Flint (Transits) o".i38 

Smith (Heliometer) o".i7 

Russell (Hypothetical) o".i02 



Table i. 



No. 


Date 


Hour 
angle 


Observer 


No. of 
expo- 
sures 


Quality of 
images 


No. of 
inter- 
polations 


I 
2 

3 
4 

5 


Mar. 29, 1912 
Mar. 31, 1912 
Apr. 24, 1912 
Apr. 30, 1912 
May 4, 1912 


hr. min. 

+0 42 
42 
6 
12 
6 


B. 
B. 
B. 
B. 

Mt. 


3 

I 

3 
3 
3 


I 

3 

5 

5 

5-1 









6 

7 


July II, 1912 
July 27, 1912 


+0 15 
24 


M. 
B. 


3 
2 


3 
3 


I 




8 

9 
10 


Mar. 17, 1913 
Mar. 18, 1913 
Apr. 25, 1913 


+0 

40 


M. 
B. 

M. 


2 
3 
3 


3 

3 







II 
12 
13 
14 
15 


June 28, 1913 
July 4- 1913 
July II, 1913 
July 14, 1913 
July 16, 1913 


+0 
-0 18 
36 
+0 6 
-0 30 


S. 
B. 
B. 
B. 
B. 


3 
3 
3 
3 
3 


5 
2 

3 
2 
2 


2 

2 
I 
I 




Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(V) 


by 


I 


•4 


-2.78 


+0.776 


+ 0.922 


.004 


M. 


2 


•5 


2.76 


•754 


.926 


.000 


S. 


3 


•9 


2.52 


•434 


.911 


.001 


S. 


4 


• 5 


2.46 


•340 


.904 


.002 


M. 


5 


•7 


2.42 


.276 


.900 


.004 


S. 


6 


.6 


-1.74 


-0.768 


.866 


.007 


S. 


7 


.6 


1.58 


•915 


•854 


.005 


S. 


8 


• 7 


+ 0.75 


-fo.88o 


.787 


.006 


S. 


9 


•9 


.76 


.872 


.807 


.014 


S. 


10 


•7 


1. 14 


.432 


.768 


.OQ2 


S. 


II 


.6 


+ 1.78 


— 0.604 


.727 


.000 


S. 


12 


.8 


1.84 


.682 


■723 


.000 


S. 


13 


.6 


I.9I 


.765 


.711 


.008 


vS. 


14 


•9 


1.94 


.798 


.719 


.002 


S. 


15 


I.O 


1.96 


.818 


.719 


.003 


M. 



DETERMINATION OF PARALLAXES OF FIFTY STARS 75 



COMPARISON STARS. 



No. 


^ 


Y 


Depend- 
ence 


Diameter 


B. D. No. 


Mag- 
nitude 


I 

3 
4 

8 

TV 


+ 119.236 

— 218.970 

156.748 

+ 256.483 
20.664 


+ 103.705 
75-691 

— 114. 182 
65.216 

+ 8.353 


0.29 
0.24 
0.20 
0.27 


0.48 
0.26 

0.54 
0.78 
0.61 


+31° 2887 

32 2764 
31 2892 


9.2 

9.0 

8.4 



Normal equations: 



Solution: 



38.915M— 0.275c— 6. 2l87r= —1.824. 

+ 10.408 —0.767 =+8.390. 
+5.207 =-0.285. 



p. e. unit weight =to."oi5. 



IX = — o".i79 =to."oo3. 
c = +o .806. 

+o".o86±o".co8. 



B. D. + 28° 2624. 2 2107. (i6'^48™, +28° 50'.) 
Mag. 8.0 - 8.5. 

The measures were in longitude. This star is a binary with 
a period yet to be determined. 

Russell finds a hypothetical parallax of + o" .022 for this star. 

Table i. 











No. of 




No. of 






Hour 




expo- 


Quality of 


inter- 


No. 


Date 


angle 


Observer 


sures 


images 


polations 






hr. min. 










I 


Mar: 3, 1914 


-0 23 


P- 


3 


4 


I 


2 


Apr. 5, 1914 


+ 28 


P. 


3 


5 


I 


3 


Apr. 10, 1914 


30 


P. 


3 


5 





4 


Apr. 13, 1914 


50 


M. 


2 


5 


I 


5 


Apr. 17, 1914 


-0 3 


P. 


2 


5 





6 


July 19, 1914 


+ 1 20 


M. 


2 


2 





7 


. uly 2S, 1914 


I 


M. 


3 


5 





8 


. uly 29, 19 14 


52 


M. 


2 


5 





9 


July 30, 19 14 


I 25 


M. 


2 


5 





10 


July 31, 1914 


50 


M. 


3 


5 





II 


Aug. 6, 1914 


I 15 


M. 


2 


5 





12 


Aug. 9, 1914 


I 35 


M. 


3 


5-2 


I 


13 


Mar. 31, 1915 


+0 30 


Ma. 


3 


3 





14 


Apr. 4, 1915 


-0 34 


P. 


3 


5 






Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(V) 


by 


I 


•9 


-1. 14 


+ 0.982 


+ 0.054 


.005 


M. 


2 


.9 


0.81 


.757 


•045 


.004 


M. 


3 


•9 


.76 


.699 


.045 


.004 


M. 


4 


.8 


•73 


.662 


.047 


.002 


M. 


5 


.8 


.69 


.610 


.046 


.002 


M. 


6 


.9 


+0.24 


-0.797 


.051 


.005 


M. 


7 


.6 


-33 


.882 


.054 


.008 


M. 


8 


.8 


•34 


.890 


.047 


.001 


M. 


9 


•7 


•35 


.898 


•051 


•005 


M. 


10 


.7 


•36 


•905 


.041 


•005 


M. 


II 


.8 


.42 


.946 


- .037 


.009 


M. 


12 


•7 


.45 


•963 


.038 


.008 


M. 


13 


.9 


+2.79 


+O.81I 


.042 


.004 


M. 


14 


•9 


2.83 


.771 


.050 


.004 


M. 







COMPARISON 


STARS. 












Depend- 






Mag- 


No. 


X 


Y 


ence 


Diameter 


B. D. No. 


nitude 


I 


+ 80.263 


+ I27.7II 


0.478 


0.62 


+ 28° 2626 


9-0 


2 


- 54-985 


9I.9II 


0.093 


0.69 


28 2622 


8.8 


3 


49.080 


9.361 


O.III 


0.30 






5 


+ 23.803 


-228.982 


0.318 


0.41 




j 


TT 


35-423 


2.164 




0.55 




! 



Normal equations : 

11.300C+ 3.3i7M-o.oi67r = o.527. 
+ 17.970 —0.418 =0.142. 
+ 7.774 =0.009. 
Solution : M = — o".oo3 =*= o".oo4. 

c = +o .047. 

7r= +0". 006 ±0". 006. 
p. e. unit weight ±o".oi7. 



B.D. + 33°2864. u Herculis. (171^ I3'^.6, + 33° 12'.) 
Mag. var. f^ = — 0^0016; — o".oi3. Spectrum B3 • 

The measures are in longitude. This is a spectroscopic binar}- 
No other parallax of this star has been published. 

Table i. 



No. 


Date 


Hour 
angle 


Observer 


No. of 
expo- 
sures 


Quality of 
images 


No. of 
inter- 
polations 


I 
2 

3 
4 


Apr. 23, 1914 
Apr. 30, 1914 
May 2, 1914 
May 18, 1914 


hr. mill. 
+ 

-0 24 

+ 

55 


P. 
P. 

s. 

M. 


3 
3 

3 
2 


5 
5 

3 
4 








5 
6 

7 
8 

9 


July 28, 1914 
July 29, 1914 
Aug. 15, 1914 
Aug. 17, 1914 
Aug. 19, 1914 


+ 1 38 
I 17 
30 
25 
25 


M. 

M. 

P. 

P. 

P. 


3 
3 
3 
3 
3 


4 
4 
- 5 
2 
2 









10 
II 
12 


Apr. 4, 19 1 5 
Apr. 14, 1915 
Apr. 15, 1915 


-0 33 
20 
28 


P. 

Ma. 

P. 


3 
3 
3 


4 
4 
4 








DETERMINATION OF PARALLAXES OF FIFTY STARS 



Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


M easured 


No. 


(P) 


(T) 


(P) 


(m) 


(V) 


by 


I 


I.O 


-1-37 


+0.636 


-0.139 


.005 


P. 


2 


I.O 


1.30 


•541 


•131 


.000 


P. 


3 


1.0 


1.28 


.512 


.130 


.003 


P. 


4 


.8 


1. 12 


.255 


.133 


.001 


P. 


5 


.8 


-0.41 


-0.803 


.135 


.001 


P. 


6 


.8 


0.40 


.813 


.119 


.005 


P- 


7 


I.O 


0.23 


•949 


•125 


.003 


P. 


8 


I.O 


0.21 


.962 


.120 


.002 


P. 


9 


I.O 


0.19 


.969 


.116 


.006 


P. 


10 


.8 


+2.09 


+0.850 


•134 


.004 


P. 


II 


I.O 


2.19 


•751 


•125 


.004 


P. 


12 


.8 


2.20 


•739 


.130 


.001 


P. 



COMPARISON STARS. 









Depend- 






Mag- 


No. 


X 


Y 


ence 


Diameter 


B. D. No. 


nitude 


I 


-147.638 


-155-877 


0.129 


0.63 


+32° 2877 


8.3 


2 


143-925 


48.464 


0.170 


0-39 


332860 


9-3 


3 


96.408 


+ 24.969 


0.202 


0-43 






8 


+ II6.2I8 


289.822 


0.320 


0.61 


33 2868 


9.0 


9 


271-755 


— 110.448 


0.179 


1.03 


332871 


7.8 


TT 


22.713 


+ 49-872 




0.39 







Normal equations; 



Solution 



II. 000c— 0.502ju—0.2577r= —1.406. 

+ 18.766 +3.036 =+0.076. 
+6.399 = -0.004. 



p. e. unit weight =to".oi6 



fj. = +0". 008 ±0". 004. 
c= —o .128. 

7r= —0", 031=1=0". 007, 



B.D. + 61^1678. 26Draconis - ,5962. (17^ 34- + 61° 58'.) 
]\Iag. 5.31. ^ = + 0^035; — o".50. Spectrum F. 

The measures are in longitude. This is a binary star. The 
components form a combined image, which is sensibly circular, 
and which was bisected in the measuring. Chase found the 
parallax of this star to be + o''.o8. The hypothetical parallax 
computed by Adams and by Russell is, respectively, + o".09 and 
+ o".040. 



Table i. 



No. 


Date 


Hour 

angle 


Observer 


No. of 
expo- 
sures 


Quality of 
images 


No. of 
inter- 
polations 






hr. min. 










I 
2 


Mar. II, 1913 
May I, 1913 


— 42 
+0 24 


B. 
B. 


2 
3 


5 
2 






3 
4 
5 
6 


July II, 1913 
July 16, 1913 
July 18, 1913 
July 21, 1913 


— 36 
30 

12 
12 


B. 
B. 
B. 
B. 


2 
3 

3 
3 


2 

5 
4 
4 








7 
8 

9 

10 

II 


Mar. 20, 19 14 
Apr. 3, 1914 
Apr. 18, 1914 
Apr. 22, 1914 
Apr. 30, 1914 


— 6 

15 

+0 15 

— 10 

+0 15 


M. 
M. 

M. - 
S. 
P. 


I 
3 
3 
3 
3 


3 
2 

2 

I 
5 









12 

13 
14 
15 
i6 


Apr. 7, 1915 
Apr. 14, 1915 
Apr. 15, 1915 
Apr. 21, 1915 
May 9, 1915 


-0 15 

+0 20 

5 

25 

-0 3 


Ma. 

Ma. 

P. 

Ma. 

P. 


2 
2 
2 
2 
2 


2 
4 
5 
3 
5 





I 





17 

i8 

19 

20 


July 16, 1915 
July 18, 1915 
July 23, 19 1 5 
July 24, 1915 


+0 20 
2 
II 

-0 35 


M. 
M, 
M. 

Ma. 


3 
3 
3 
3 


5 
4 
5 
5 








21 


Apr. 30, 1916 


-0 7 


P. 


3 


5 






Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(v) 


by 


I 


.6 


-5-23 


+0.896 


+0.039 


.001 


P. 


2 


I.O 


4.72 


.250 


.060 


.024 


P. 


3 


.6 


—4.01 


-0.816 


.048 


.021 


P. 


4 


•9 


3-96 


.864 


.008 


.019 


P. 


5 


.5 


3-94 


.882 


.015 


.012 


P. 


6 


.5 


3-91 


.906 


.020 


.007 


P. 


7 


•5 


-1.49 


+0.822 


.087 


.001 


P. 


8 


•5 


1-35 


.666 


.064 


.023 


P. 


9 


.8 


1.20 


458 


.068 


.018 


P. 


10 


•5 


1. 16 


•395 


.082 


.003 


P. 


II 


•5 


1.08 


.269 


.073 


.Oil 


P. 


12 


.6 


+2.34 


+0.616 


.135 


.001 


P. 


13 


1.0 


2.41 


.521 


.156 


.023 


P. 


14 


.6 


2.42 


•507 


.128 


.005 


P. 


15 


•5 


2.48 


.414 


.142 


.010 


P. 


16 


•5 


2.66 


.124 


.121 


.008 


P. 


17 


•9 


+3-34 


— 0.860 


.138 


.017 


P. 


18 


•5 


3-36 


.878 


.118 


.003 


P. 


19 




341 


.917 


.119 


.002 


P. 


20 


•5 


342 


.924 


.124 


•003 


P. 


21 


.8 


+ 6.23 


+0.257 


.161 


.016 


P. 



DETERMINATION OF PARALLAXES OF FIFTY STARS 79 



COMPARISON STARS. 









Depend- 






Mag- 


No. 


A' 


Y 


ence 


Diameter 


B. D. No. 


nitude 


2 


-171.004 


+ 83.260 


+0.829 


+ 0.55 


+56° 1672 


9.4 


3 


85.070 


29.056 


•390 


.84 


56° 1675 


8.5 


4 


92.256 


- 94-079 


-0.845 


•54 


56^ 1673 


9.3 


7 


+ 166.157 


7.170 


+0.323 


.62 


56° 1680 


9.4 


8 


182.172 


11.067 


•303 


.55 


56° 1681 


.9.3 


TT 


II.94I 


+ 154-109 




.62 







Normal equations: 



Solution; 



13.500^+ o.350M-o.5787r = 1.248. 

+ 162.230 —0.330 =2.121. 

+6.124 =0.047. 



p. e. unit weight =fco".04i. 



^l = +o".o6i =fco".oo3. 

c = +o .093. 

TT = +o".o8o ± o".oi6. 



B.D. +2°3482. 7oOphiuchi. {18^0^.4, + 2° 2>i'-) 
Mag. 4.07. // = +0^ .0169; — i".i02. Spectrum K. 

The measures are in longitude. This is a binary with a period 
of 86.66 years. Only the brighter component was measured. 
The following" parallaxes have been published : 

Schor (Heliometer) +o".286 

Krueger (Heliometer) +o".i50 

Flint (Transits) +o".i9 

Slocum (Photography) +o".2i2 

Mitchell (Photography) +o".i65 

Adams (Hypothetical) +o".22 

Table i. 



No. 


Date 


Hour 
angle 


Observer 


No. of 
expo- 
sures 


Quality of 
images 


No. of 
inter- 
polations 


I 
2 

3 

4 


Apr. 17, 1914 
Apr. 30, 19 14 
May 2, 1914 
May 9, 19 14 


hr. mill. 
+ 

43 
2 
25 


^ P. 
P. 

s. 
s. 


I 

3 
3 
2 


2 

2 

3 

I 









7 
8 


Aug. 17, 1914 
Aug. 23, 19 14 
Aug. 30, 19 14 
Aug. 31, 19 14 


+0 53 
8 

34 

1 6 


p. 
p. 
p. 
p. 


3 
3 
3 

3 


2 

4 

5^ 




I 





9 


May 9, 1915 


+0 17 


p. 


3 


4 





10 
II 
12 


July 23, 1915 
Aug. 13, 19 15 
Aug. 16, 1915 


+0 40 
45 
43 


M. 
P. 
P. 


3 
3 
3 


5 

t 








8o 



JOHN A. MILLER 



Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(v) 


by 


I 


.6 


— 2.02 


+0.892 


+ 0.126 


•003 


P. 


2 


•7 


1.86 


.772 


.131 


.004 


P. 


3 


I.O 


1.84 


.750 


.128 


.002 


P. 


4 


•9 


1.77 


.666 


.127 


.004 


P. 


5 


•5 


0.77 


-0.818 


.070 


.003 


P. 


6 


1.0 


0.71 


.872 


.072 


.000 


P. 


7 


•7 


0,64 


•925 


•074 


.004 


P. 


8 


.8 


0.63 


.931 


- .069 


.010 


P. 


9 


.8 


+ 1.88 


+0.668 


.141 


.oil 


P. 


10 


•5 


+2.63 


-0.503 


.124 


.012 


P. 


II 


1.0 


2.84 


•775 


.106 


.003 


P. 


12 


1.0 


2.87 


.806 


.103 


.001 


P. 







COMPARISON 


STARS. 






No. 


X 


Y 


Depend- 
ence 


Diameter 


B. D. No. 


Mag- 
nitude 


4 
7 
9 

TT 


+ 128.692 

71.384 
— 200.076 

28.662 


+ 32.881 

— 141. 125 
+ 108.243 

— _l.T.68c; 


0.033 
0.591 
0.376 


0.53 
0.47 
0.47 

O.cS 


+ 2° 3487 
2 3483 

2 3479 

TT 


9.5 

9-3 
9-5 



Normal equations: 



Solution : 



9.500C+ 0.535m 
+35-070 



p. e. unit weight ±o".oi9. 



+ 0' 
+0 
+0' 



■i.5497r = 1.001. 

6.880 =0.065. 

+5-979 =0.005. 

.036^0^.004. 

.III. 

.181 ±0". 009. 



B. D. + 32° 3267. Bradley 2388 ■■ 
Mag. 5.21. 11 = +0^0137; 

The measures were made in 



-- /%48 (18^53^-3, + 32°47'-) 
- o".i6o. Spectrum G. 

lonmtude. This is a binary 



with a period of 45.85 years. The combined image of the two 
components is very slightly elongated. In the measurements we 
attempted to bisect this elongated image. 

Other parallaxes of this star published are : 

Flint (Transits) +o".oi 

Russell (Hypothetical) ' +o".o7i 



DETERMINATION OF PARALLAXES OF FIFTY STARS 8i 



Table i, 



No. 


Date 


Hour 
angle 


Observer 


No. of 
expo- 
sures 


Quality of 
images 


No. of 
inter- 
polations 


I 
2 

3 
4 


May II, 19 13 
May 14, 1913 

May 18, 19 13 
June 2, 1913 


hr. mill. 

-0 6 

+0 30 

18 

36 


B. 

M. 
B. 

S. 


3 
2 

3 
3 


5 
4 
4 
5 








I 


May 2, 19 14 
May 20, 19 14 


-0 7 

+0 36 


S. 

s. 


3 
3 


5 
4 


I 




7 
8 

9 

10 

II 

12 


Aug. 15, 1914 
Aug. 23, 19 14 
Aug. 30, 19 14 
Sept. 2, 1914 
Sept. 4, 1914 
Sept. 5. 1914 


+0 25 
4 
12 

— 20 
+0 6 

— 29 


p. 
p. 
p. 
p. 

p. 
p. 


2 
3 
3 
3 
3 
3 


4 

5 
5 
5 
5 
5 



2 



4 

I 



Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(v) 


by 


I 


•5 


-3.01 


+0.867 


-0.093 


.010 


M. 


2 


•7 


2.98 


.840 


•073 


.010 


S. 


3 


.9 


2.94 


.801 


.084 


.000 


S. 


4 


•5 


2.79 


.624 


.089 


.002 


M. 


5 


.7 


+ 0.55 


+ 0.935 


.046 


.001 


S. 


6 


•5 


0.73 


.783 


.046 


.003 


M. 


7 


.6 


+ 1.60 


-0.541 


.085 


.009 


M. 


8 


•5 


1.68 


.649 


.071 


.008 


S. 


9 


•7 


1-75 


.735 


•073 


.007 


M. 


10 


•7 


1.78 


.768 


.087 


.006 


M. 


II 


.6 


1.80 


.789 


.089 


.009 


M. 


12 


.7 


1. 81 


•799 


.070 


.Oil 


M. 



COMPARISON STAES. 









Depend- 






Mag- 


No. 


X 


Y 


ence 


Diameter 


B. D. No. 


nitude 


2 


+ 31-982 


-145-131 


0.323 


0.42 






5 


-155459 


162.803 


0.199 


0.86 


+ 18=3276 


8.7 


6 


126.512 


55-970 


0.146 


0.91 


18° 3275 


8.5 


II 


+102.375 


+ 170.457 


0.157 


0.67 


18° 3263 


9.0 


12 


147.612 


193.446 


0.175 


0.57 


19^3263 


9.1 


TV 


2.884 


- 26.725 




0.6d 







Normal equations: 

7.600c- 0.264M+ o.3677r= -0.575. 
+34.441 -10.190 =+0.083. 
+ 4.561 =-0.005. 
Solution: /x = +0". 046^0". 006. 

c = —o .077. 

7r= +0".I26±0".0I7. 

p. e. unit weight ±o".02i. 



JOHN A. MILLER 



B.D. +44°3234- 5 Cygni. (i9h4i™.9, + 44° 53'.) 
Mag. 2.97. ju = +0^0050; +o".037. Spectrum A. 

The measures are in longitude. This is a binary of very 
long period. In order to choose the comparison stars we adopted 
the method described on pages 10 to 16 of this paper. The 
preliminary measures indicated that a field consisting of stars 
numbered 2, 6, 7, and 10 should give a larger parallax than any 
other symmetrically arranged field on the plate, and that a field 
consisting of stars numbered i, 3, 6, and 9 should give a smaller 
parallax than any other symmetrically arranged field. In order to 
test the method prescribed in Part II of this paper we decided to 
measure both fields, and, in order that the final parallax should 
not be prejudiced by errors made in the measures for the determi- 
nation of the field, we rejected, for the purpose of determining the 
parallax, all but three of the plates used in choosing the field and 
measured seven additional plates. 

The data and reductions for the first field (stars 2, 6, 7, and 
10) are given in Tables i and 2, and following these are the 
normal equations and solution. The same items are given for 
the field i, 3, 6, and 9 in Tables 3 and 4. The normal equa- 
tions and solution for this field follow the tables. One plate in 
the first series is not in the second and three in the second series 
are not in the first. This seemed desirable because of the quality 
of the images of some of the comparison stars. The results for 
the first field are 71 = + 0^.049 ± o".oo8 and for the second tt - 
o" .ooy ± o".oi9, which indicate that the method really tells us 
something as to the relative distance of comparison stars. A hypo- 
thetical parallax of this star computed by Russell is o''.03i. 

Table i. 



No. 


Date 


Hour 
angle 


Observer 


No. of 
expo- 
sures 


Quality of 
images 


No. of 
inter- 
polations 


I 
2 


Aug. 30, 1914 
Sept. 9, 1914 


hr. min. 
+ 

-0 56 


P. 
P. 


3 
3 


5 
2 




I 


3 
4 
5 
6 


May 19, 1915 
June 9, 1915 
June 14, 1915 
June 17, 1915 


+0 20 



20 


Ma. 
Ma. 
Ma. 
M. 


2 
3 

3 
3 


2 
4 

5 
5 



2 




7 
8 

9 
10 


Sept. 7. 1915 
Sept. 10, 19 15 
Sept. 24, 1915 
Sept. 29, 19 15 


+0 23 

^ I 

6 
15 


P. 
S. 
P. 
P. 


2 

3 
2 

3 


. 4 
5 
5 
3 



I 

I 



DETERMIXATIOX OF PARALLAXES OF FIFTY STARS 83 



Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


Xo. 


(P) 


(T) 


(P) 


(m) 


(v) 


by 


I 


•7 


-2.67 


-0.373 


-0.049 


.004 


M. 


2 


.8 


•257 


.523 


.042 


.004 


M. 


3 


•7 


-.005 


+0.985 


•043 


.006 


M. 


4 


.7 


+0.16 


.847 


•037 


.001 


M. 


4 


•7 


0.21 


•799 


.038 


.001 


M. 


6 


.6 


0.24 


.766 


.034 


.006 


M. 


7 


.8 


+ 1.06 


-0.492 


.044 


.010 


M. 


8 


•7 


1.09 


.535 


.058 


.002 


M. 


9 


.8 


1.23 


.718 


.062 


.005 


M. 


10 


.8 


1.28 


•775 


.060 


.002 


M. 



COMPARISON STARS. 



No. 


A- 


i' 


Depend- 
ence 


Diameter 


B. D. Xo. 


xMag- 
nitude 


2 

6 

7 
10 

TT 


-231-911 
+ 184-995 

- 67.107 
+ 114.024 

- 63.568 


- 75-842 

+ 66.903 

196.163 

-187.223 

3-437 


0.396 

0-133 
0.276 

0.195 


0.47 
0.48 
0.50 

0.54 
0.76 


+44° 3246 
44^3245 


9-5 
9-5 



Normal equations: 



Solution ; 



7.300f+ o.o62M-o.3407r= -0.345. 

+ 14.611 —0.267 =—0.040. 

+3-584 =+0.054. 



p. e. unit weight =to".oi6. 



M=-0' 


.Oil =i=o".oo4 


r= — 


.047. 


7r = +0' 


.049±o".oo8 



Table 



No. 


Date 


Hour 

angle 


Observer 


Xo. of 
expo- 
sures 


Quality of 
images 


No. of 
inter- 
polations 


I 
2 


May 30, 19 14 
June 6, 1914 


hr. min. 

+0 5 
10 


S. 
S. 


2 

3 


2 

2 


I 
2 


3 
4 


Sept. 5, 1914 
Sept. 9, 1914 


+0 . 

-0 56 


P. 
P. 


2 
3 


5 
2 


I 
2 


5 
6 

7 
8 


May 19, 19 15 
June 9, 19 15 
June 14, 19 15 
June 17, 1915 


+0 30 


20 


Ma. 
Ma. 
Ma. 
M. 


3 

3 


2 

4 
5 
5 


2 





9 
10 
II 

12 


Sept. 10, 1915 
Sept. 22, 1915 
Sept. 24, 1915 
Sept. 29, 1915 


+0 8 
20 
6 
15 


S. 
P. 

I: 


3 

2 

3 
3 


5 
2 

5 
3 









84 



JOHN A. MILLER 









Table 4 










Weight 


Time in 


Parallax 










of plate 


100 davs 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(v) 


by 


I 


-5 


-3.01 


+ 0.925 


— 0.192 


-015 


M. 


2 


•9 


2.94 


.872 


.186 


.009 


M. 


3 


•9 


-2.03 


— 0.466 


•153 


•023 


M. 


4 


.8 


1.99 


•523 


.180 


•005 


M. 


5 


•7 


+0.53 


+0.985 


.142 


•023 


M. 


6 


.8 


•74 


•847 


.164 


.001 


M. 


7 


.8 


•79 


•799 


.164 


.000 


M. 


8 


.8 


.82 


.766 


.166 


.002 


M. 


9 


.8 


+1.67 


-0.535 


.176 


.012 


M. 


10 


-7 


1.79 


.694 


•154 


.009 


M. 


II 


.8 


1. 81 


.718 


.160 


.003 


M. 


12 


.6 


1.86 


•775 


.184 


.021 


M. 



COMPARISON STARS. 



No. 


.Y 


Y 


Depend- 
ence 


Diameter 


B. D. No. 


Mag- 
nitude 


I 

3 
6 

9 

TT 


-194.470 

151.030 

+251-930 

93-570 

3-367 


+ 180.158 

— 106.019 
+ 88.088 

— 162.226 

+ 17-748 


+0.283 
.2X8 

.283 

.216 


0-53 
0.51 
0.48 

0.79 
0.76 


+44° 3222 
44° 3227 
44° 3246 
44° 3238 


9.1 

9-5 
9-5 
8.9 



Normal equations 

Solution : 

p. e, unit weight =to".04 



9.10OC— 0.i66yu + i.0787r= —1.526. 

30.039 -3.642 =+0.120. 

5.100 =-0.185. 



11 = +o".oi5 =to".oo8. 

c = — o .168. 

TT = +o".oo7 ±o".oi9. 



B. D. +44° 3242. (i9V".8, +44° 5i.'8-) 
Mag. 9.2. 

The measures are in longitude. This star was on the plates 
with 8 Cygni. \Mien the comparison stars for 8 Cygni were 
being selected by the method described in pages 10 to 16, it 
seemed that this star should give a sensible positive parallax, 
and it was measured and reduced for that reason, which seems 
to indicate that absolute reliance cannot be placed in the relative 
parallaxes of comparison stars, determined as described in this 
paper. Xo other parallax of this star has been published. 



DETERMINATION OF PARALLAXES OF FIFTY STARS 85 



Table i. 



No. 


Date 


Hour 

angle 


Observer 


No. of 
expo- 
sures 


Quality of 
images 


No. of 
inter- 
polations 


2 


May 30, 19 14 
June 6, 19 14 


hr. ynin. 

+0 5 
10 


S. 
S. 


3 
3 


2 
2 


I 
I 


3 
4 


Sept. 5, 1914 
Sept. 9, 1914 


+0 2 
-0 56 


P. 
P. 


2 
3 


5 
2 


I 


5 
6 

7 
8 


May 19, 1915 
June 9, 1915 
June 14, 1915 
June 17, 1915 


+0 20 


20 


Ma. 

Ma. 
Ma. 
M. 


2 

I 

3 


2 

4 
5 
5 




, 




9 

10 
II 
12 


Sept. 10, 1915 
Sept. 22, 1915 
Sept. 24, 1915 
Sept. 29. 1915 


+0 8 
20 
6 
15 


S. 
P. 
P. 
P. 


3 
2 

3 
3 


5 
2 

5 
3 









Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(V) 


by 


I 


•7 


-3.01 


+0.925 


+0.030 


.004 


M. 


2 


•7 


2.94 


.872 


.040 


.006 


M. 


3 


.6 


-2.03 


— 0.466 


.041 


.000 


M. 


4 


.7 


1.99 


•523 


.038 


.003 


M. 


5 


.8 


+0.53 


+0.985 


•054 


.006 


M. 


6 


.8 


0.74 


.847 


•043 


.006 


M. 


7 


.9 


0.79 


•799 


•044 


.005 


M. 


8 


.8 


0.82 


.766 


.052 


.003 


M. 


9 


.8 


+ 1.67 


-0.535 


.051 


.005 


M. 


10 


.7 


1.79 


.694 


•054 


.003 


S. 


II 


.8 


1. 81 


.718 


.060 


.003 


M. 


12 


.8 


1.86 


.775 


.063 


.006 


M. 







COMPARISON 


STARS. 












Depend- 






Mag- 


No. 


X 


Y - 


ence 


Diameter 


B. D. No. 


nitude. 


5 


- 80.254 


- 32.019 


0.307 


1. 14 


+44° 3236 


8.0 


6 


+ 103.195 


+ 178.820 


0.338 


0.48 


44° 3246 


9-5 


9 


- 55-165 


- 71-494 


0.231 


0.79 


44° 3238 


8.9 


10 


+ 2>2.22J^ 


75-306 


0.124 


0.54 


44° 3245 


9-5 


X 


1-538 


+ 24.763 




0.70 







Normal equations: 



Solution: 



9.IOOC+ I.I32 + I.3027r = 0.436. 

+29.262—4.235 =0.182. 
+5.306 =0.032. 



p. e. unit weight ±o".oi4. 



M = +0". 019 ±0". 003. 
c = +o .478. 

7r= — 0".0I2=t0".007. 



86 



JOHN A. MILLER 



B. D. + 14° 4369. ^ Delphini. (20^^ 32^^.9, + 14° I5'-) 
Mag. 372. n = +0^ .0374; — o".037. Spectrum F5. 

The measures are in longitude. This is a binary with a 
period of 26.79 years. The combined image of the components 
did not show any sensible elongation. 

Fhnt found for the parallax of this star a value of - o".02. 
Russell's hypothetical parallax of this star is + o".038. 

Table i. 



No. 


Date 


Hour 
angle 


Observer 


No. of 
expo- 
sures 


Quality of 
images 


No. of 
inter- 
polations 






hr. min. 










I 


June 2, 1913 


+ 


s. 


3 


4 


I 


2 

3 


Sept. 24, 1913 
Sept. 28, 1913 


— 10 

28 


s. 

M. 


3 
3 


4 
3 






4 

5 
6 

7 
8 


Aug. 30, 1914 
Sept. 2, 1914 
Sept. 5, 1914 
Sept. 16, 1914 
Sept. 26, 1914 


+0 5 

8 
3 

-0 30 


P. 

P. 

P. 

M. 

P. 


3 
3 

2 

3 
3 


5 
3 
4 
3 
4 




I 


I 
I 


9 


June 9, 1915 


+0 20 


Ma. 


2 


4 





10 


June 17, 1915 


35 


M. 


3 


5 





II 


June 20, 19 1 5 


40 


M. 


2 


4 





12 


June 23, 19 1 5 


I 5 


Ma. 


3 


4 






Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(V) 


by 


I 


•9 


-4.61 


+0.902 


+0.070 


.001 


P. 


2 


.6 


-3-47 


-0.724 


.065 


.006 


P. 


3 


.8 


3-43 


.769 


.071 


.001 


P. 


4 


•9 


—0.07 


-0-374 


.084 


.008 


P. 


5 


.8 


0.04 


.420 


.096 


.004 


P. 


6 


•9 


O.OI 


.466 


.097 


.006 


P. 


7 


I.O 


-fo.io 


.622 


.094 


.002 


P. 


8 


.7 


0.20 


•745 


.083 


.009 


P. 


9 


.7 


+2.76 


+0.847 


.100 


.012 


P. 


10 


■9 


2.84 


.766 


.119 


.006 


P. 


II 


•9 


2.87 


.732 


.105 


.007 


P. 


12 


.8 


2.90 


.696 


.121 


.009 


P. 



DETERMINATION OF PARALLAXES OF FIFTY STARS 87 



COMPARISON STARS. 









Depend- 






Mag- 


No. 


X 


Y 


ence 


Diameter 


B. D. No. 


nitude 


3 


+ 143.693 


+ 156.310 


-0.213 


0.35 






5 


-170.681 


- 47-056 


+0.040 


0.64 


+ 14° 4361 


9.1 


6 


137.768 


90-455 


.283 


0.62 


14° 4366 


9.4 


10 


+ 140.609 


+ 13.912 


-374 


0.50 






II 


209.178 


74-790 


•251 


0.50 






21 


-185.032 


-107.504 


.265 


0.49 






TV 


20.245 


65.178 




0.82 







Normal equations: 



Solution 



9.90OC+ o.552/x+o.0257r =0.920. 

+62.535 +6.850 =0.441. 

+4.657 =0.058. 



p. e. unit weight ±o".022. 



+0". 028^0". 003. 
+0 .093. 
+o".oi6±o".oii. 



B. D. + 35° 4234. X Cygni. (20^ 39-.5, + 35° 14'.) 
Mag. var. Spectrum Fsp. 

The measures are in longitude. This is a spectroscopic binary. 
No other parallax of this star has been published. 



Table i. 











No. cf 




No. of 






Hour 




expo- 


Quality of 


inter- 


No. 


Date 


angle 


Observer 


sures 


images 


polations 






hr. min. 










I 


Sept. 8, 1914 


-Q 4 


P. 


3 


2 


I 


2 


Sept. 9, 1914 


25 


P. 


3 


2 


I 


3 


Sept. 10, 1914 


34 


P. 


2 


5 


I 


4 


June 22, 1915 


+0 12 


M. 


3 


5 





5 


June 24, 1915 


25 


M. 


3 


5 


I 


6 


June 27, 1915 


25 


M. 


I 


5 





7 


June 2S, 1915 


23 


Ma. 


2 


5 





8 


July 5, 1915 


10 


Ma. 


3 


5 





9 


July 6, 1915 


15 


M. 


2 


' 





10 


Sept. 7, 1915 


+0 32 


P- 


3 


5 


I 


II 


Oct. 9, 1915 


15 


Ma. 


3 


2 


2 


12 


Oct. 10, 1915 


30 


S. 


3 


3 





13 


Oct. 17, 1915 


25 


s. 


3 


5 





14 


Oct. 24, 1915 


50 


M. 


2 


3 





15 


Oct. 28, 1915 


30 


M. 


3 


5 






JOHN A. MILLER 









Table 2. 








Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(v) 


by 


I 


I.O 


-2.77 


-0.322 


+ 0.084 


.008 


P. 


2 


.6 


2.76 


•339 


.089 


.003 


P. 


: 3 


1.0 


2.75 


•354 


.101 


.009 


P. 


4 


I.O 


+ 0.10 


+0.842 


.101 


.007 


P. 


5 


I.O 


0.12 


.823 


.088 


.006 


P. 


6 


•5 


0.15 


.791 


.091 


.003 


P. 


7 


I.O 


0.16 


.780 


.090 


.004 


P. 


8 


•9 


0.23 


.699 


-.097 


.003 


P. 


9 


•7 


0.24 


.686 


.099 


.005 


P. 


10 


.8 


+0.87 


-0.301 


.095 


.000 


P. 


II 


•9 


1. 19 


.752 


.083 


.012 


P. 


12 


I.O 


1.20 


•763 


.089 


.006 


P. 


13 


I.O 


1.27 


.833 


.099 


.004 


P. 


14 


•5 


1-34 


.892 


.102 


.007 


P. 


15 


•9 


1.38 


.919 


.100 


.005 


P. 







COMPARISON 


STARS. 












Depend- 






: Mag- 


No. 


X 


F 


ence 


Diameter 


B. D. No. 


;nitude 


I 


-124.075 


+ 151-387 


0.062 


0.58 




' 9.0 


4 


87.294 


56.655 


0.166 


0.40 


+35° 4228 


9-4 


7 


115-753 


- 79-641 


0.354 


0.50 


34° 4129 


: 9-5 


13 


+ 106.532 


1x6. 179 


0.301 


0.66 


35° 4240 


8.7 


15 


220.592 


12.221 


O.II7 


0.44 


35° 4244 


! 9-5 


TT 


- 5-185 


45-815 




0.38 







Normal equations : 



Solution: 



p. e. 



unit weight 



12. 800c— 0.197/1- o.7i67r= +1.199. 
+27.501 —1.676 =+0.002. 
+6.390 = —0.068. 
M = +0". 004=1=0". 004. 
r = +o .094. 

7r= +O".000=to".008. 
0".02I. 



■- B. D. + 38°4343- 61 Cygni. (21^ 2-4, + 38° 15'.) 
Mag. 5.57. n = +0^3523; + 3". 242. Spectrum Ko. 

This is the parallax of the brighter component. It was 
measured in longitude. 

The parallax of the fainter component of this star was ob- 
tained at the same time, from the same set of comparison stars. 
One of the plates was rejected because the image of this com- 
ponent was too faint to measure. The results for the fainter 
component were : 

M = +i".3i3 ± o".oo8. 

7r = +0".299 ± 0".02I. 

p.e. unit weight = ± o".047. 



DETERMINATION OF PARAELANES OF FIFTY STARS 89 



The star 61 Cygni was chosen because its parahax had been 
determined many times. AA'e hoped in this way to caHbrate 
our results. 

The absohite parallax given by Kapteyn and \\'eersma for 
this star is ^ o".3ii. The hypothetical parallax computed by 
Russell for this star is + o'^336. Adams found for the larger 
component of this star a hypothetical parallax of + o".30, and for 
the smaller component a hypothetical parallax of + o".34. 

Table i. 



No. 


Date 


Hour 
angle 


Observer 


No. of 
expo- 
sures 


Quality of 
images 


Xo. of 
inter- 
polations 






hr. min. 










I 


June 8, 1912 


— I 12 


B. 


3 


3 





2 


June 10, 1912 


I 18 


B. 


2 


I 





3 


June 21, 1912 


+ 


M. 


2 


I 





4 
5 


June 22, 1912 
July 5. 1912 


-0 48 

+0 18 


B. 


3 
2 


2 
2 


2 



6 

7 
8 

9 


Oct. 3, 1912 
Oct. 6, 1912 
Oct. 10, 1912 
Oct. II, 1912 


— 20 

30 

10 

+ 




3 
3 
3 
2 


2 
3 
3 
3 





I 



10 


June II, 19 13 


+ 


M. 


2 


5 





II 


June 13, 1913 





M. 


2 


3 





12 


June 29, 1913 


12 


B. 


2 


I 





13 
14 
15 
16 


Sept. 27, 1913 
Sept. 28, 1913 
Oct. 16. 1913 
Oct. 23. 1913 


-0 5 

22 

15 

20 


M. 

AI. 
M. 


3 
3 
3 
2 


5 
5 
2 

5 









Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(v) 


by 


I 


•9 


-2.06 


+0.991 


— 2.146 


.002 


s. 


2 


.6 


2.04 


.984 


2.123 


.016 


M. 


3 


•3 


1-93 


.922 


2. 118 


.006 


M. 


■ 4 


•7 


1.92 


.915 


2. 115 


.005 


s. 


5 


•7 


1.79 


.798 


2.072 


.009 


M. 


6 


•5 


-0.89 


-0.572 


I.918 


.002 


M. 


7 


•9 


0.86 


.612 


1.920 


.010 


S. 


8 


.8 


0.82 


.665 


1.899 


.003 


M. 


9 


.5 


0.81 


.677 


1.905 


.004 


S. 


10 


.8 


+ 1.62 


+0.980 


I.IIO 


.001 


S. 


II 


.6 


1.64 


.971 


1. 122 


.016 


M. 


12 


.6 


1.80 


.859 


1.066 


.002 


M. 


13 


•9 


+2.70 


-0.482 


0.906 


.005 


S. 


14 


•7 


2.71 . 


.497 


0.893 


.007 


M. 


15 


•5 


2.89 


•734 


0.869 


.005 


M. 


16 


•7 


2.96 


.808 


0.838 


.Oil 


M. 



90 



JOHN A. MILLER 



COMPARISON STARS. 









Depend- 






Mag- 


No. 


X 


I' 


ence 


Diameter 


B. D. No. 


nitude- 


4 


+ 146.74 


+ 46.77 


0.25 


0.33 


+38° 4351 


9-5 


5 


-218.18 


38.30 


0.23 


0.24 






6 


+ 207.85 


-83.57 


0.13 


0.34 






i6 


-229.25 


53-94 


0.14 


0.32 






19 


+ 92.84 


+52.43 


0.25 


0.33 






TT 


2.55 


15-59 




0.36 







Normal equations: 



Solution ; 



4i.874,u+ 2.67or — 6.o677f = + 7.028. 

+ 10.708 +1.420 =-16.597. 

+6.724 =- 3.585. 



p. e. unit weight ^o" .02: 



M = +l' 


'.318 ±0". 004 


r = -I 


.629. 


x= +0' 


'.301 ±o".oc9 



B. D. + 37°4240. -Cygni. 
Mag 3.82 — 8.00. "+0-.0133; 



(2x1^ 10™. 8, 
+ o".427. 



r 01 01 ■) 

Spectrum F. 

The measures were in longitude. This is a binary with a 
period of 47 years. Other pubHshed parallaxes are : 
By Jost, who found it to be + o" .12. 
By Millosevich, who found it to be ^o".029. 
By Slocum and iMitchell, who obtained - o".oo6. 
By Russell, who obtained a hypothetical parallax of 

Table i. 



O .046. 













No. of 




No. of 








Hour 




expo- 


Quahtv of 


inter- 


No. 




Date 


angle 


Observer 


sures 


images 


polations 








hr. mill. 










I 


June 


I, 1912 


-0 30 


M. 


2 


3 





2 


July 


8, 1912 


+0 6 


B. 


3 


5 





3 


July 


12, 1912 


12 


B. 


2 


I 





4 


June 


30, 1913 


— 12 


S. 


3 


5 





5 


ulv 


3, 1913 


+0 


B. 


3 


I 





6 


.ulv 


7, 1913 


I 20 


S. 


2 


2 





7 


July 


8, 1913 


-I 25 


B. 


2 


I 





8 


Sept. 


28, 1913 


! —0 2 


]M. 


3 


3 





9 


Oct. 


5, 1913 


5 


M. 


3 


5 





10 


Oct. 


22, 1913 


+0 30 


P- 


2 


4 





II 


Oct. 


2, 1914 


+0 10 


U. 


3 


5 





12 


Oct. 


23, 1914 


i 15 


P. 


2 


' 2 


I 


13 


Oct. 


31, 1914 


3 


P. 


3 


5 


I 


14 


Nov. 


2, 1914 


; -0 2 


P. 


3 


4 


I 



DETERMIXATIOX OF PARALLAXES OF FIFTY STARS 91 



Table 





1 Weight 


lime in i P'arallax 












of plate 


100 davs 


factor 


Solution 


Residual 


Measured 




Xo. 


(P) 


(T)- 


(P) 


(m) 


(V) 


by 




I 


.8 


-4-65 


+ I.0I2 


-2.005 


.008 


S. 




2 


•9 


4.28 


0.787 


2.020 


.012 


S. 




3 


.7 


4.24 


0.743 


2.015 


.007 


M. 




4 


.5 


-0.71 


+0.868 


1.950 


.002 


Mt. 




5 


•7 


0.68 


.840 


1.950 


.002 


M. 




6 


.6 


0.64 


.800 


1-949 


.002 


S. 




7 


•5 


.063 


.789 


1.952 


.001 


S. 




8 


•7 


+0.19 


-0.469 


1-934 


.010 


M. 




9 


.9 


0.26 I .570 


1.946 


.002 


S. 




10 


.6 


0.43 -780 


1.949 


.007 


M. 




II 


.7 


+3.88 


-0.524 


1.888 


.0.01 


M. 




12 


•7 


4.09 


.787 


1.878 


.007 


M. 




13 ' -7 


4.17 ' .862 


1.886 


-003 


P. 




14 .8 


4.19 .S78 


1-895 


.012 


M. 






COMPARISON 


STARS. 










Depend- 






Mag- 


Xo. 


-Y 


r ence 


Diameter 


B. D 


Xo. 'nitude 


I 


+ 164.877 - 


- 20.757 0.20 


0.58 






4 


-171.266 ^ 


- 43-319 0.15 


0.42 






5 


149-515 


III. 263 1 0.23 


0.48 






6 


226.238 : 


23.694 j 0.12 


0.39 






9 


+ 131-509 


- 68.904 1 0.14 


0.54 






10 


250.632 ' 


88.614 0.16 


0.52 






TT 


2.317 H 


- -._L0_L 


o.6j. 







Normal equations: 



Solution ; 



96.084M+O.407C — I9.8047r= + 0.620. 

+9. 80S + 0.402 =—19.072. 

+ 5.906 = - 1.064. 



p. e. unit weight = ±o".02i, 



M = +0". 074 ±0". 004. 

c = -i .945. 

7r= +0". 023=^^0". 016. 



B. D. + 24°4463. /c Pegasi = /3989. (21^40^.1, -{- 2^° 11'.) 
Mag. 5.0 — 5.1. fjL = +0^.0024; +o".oo2. Spectrum F5. 

This is a verA- close binary 



The measures were in longitude 
with a period of 11.37 years, 
ponents were not elongated. 

Flint found the parallax of this star to be 
computed a hypothetical parallax of - o".043. 



The combined images of its com- 



o .02. 



Russell 



Table i. 



No. 



Date 



Hour 
angle 



Observer j 



Xo. of Xo. of 

expo- Quality of inter- 

sures images polations 



9 

lO 

II 

12 



July 8, 1912 

July 16, 1912 

Oct. 5, 1912 

Oct. 6, 191 2 

Oct. 16, 1912 

Oct. 30, 1912 

July 3, 1913 

July 8, 19 13 



Sept. 28, 
Nov. I, 



1913 
1913 



July 19, 1914 

Ju'y 2S. 1914 



hr. min. 




f 12 I 


B. 





AI 



+0 25 M. 

o 15 ^I- 
o 30 B. 



o 42 



-rO 
o 

+0 
o 

+ 1 

I 



19 
40 

10 



B. 



M. 

S. 
S 



Taile 



No. 


Weight 

of plate 

(P) 


Time in 

100 davs 

(T) 


Parallax 

factor 

(P) 


Solution 

(m) 


Residual 

(v) 


i Measured 
by 


I 
2 


•7 

•7 


-2.95 
2.87 


-f 0.790 
•699 


-f 1.020 
1.005 


•005 
.CO9 


s. 


3 
4 
5 
6 


.8 

•7 
.6 

•7 


— 2.06 
2.05 

1-95 
1.81 


-0.569 

.712 

.855 


0.990 
0.999 
0.992 
1.004 


.007 
.002 
.003 
.DIG 


S. 

s. 


7 
8 


.7 
.8 


+0.65 
0.70 


+0.843 

•793 


+ 1.028 
1.038 


.000 
.Oil 


i: 


9 
10 


.7 
•7 


+ 1.52 
1.86 


-0.464 
.870 


1.007 
1.008 


.004 
.002 


s. 


II 

12 


•9 

.q 


+446 


-ho.667 


1.037 

i.o;6 


.001 

.001 





COMPARISON" STAR; 









Deoer.G- 






Mag- 


No. 


-Y 


r 


ence 


Diameter 


B. D. Xo. 


nitude 


4 


-115.240 


+ 184.709 


0.17 


+0.53 


+ 24= 4460 


8.8 


5 


127.407 


1.598 


0.18 


0.58 


24^^ 4458 


9-0 


7 


200.322 


- 66.342 


0.17 


0.39 






10 


+ 206.999 


194.842 


0.24 


0.67 






II 


235-972 


+ 74-877 


0.24 


0.35 






TT 


30.719 


- 7.614 




0-75 







Normal equation; 



64.074.: + i.S59f +4.7657r=2.2i6. 













+8. 90S +0 

+4 


535 
443 


= 9.035 
= 0.627 


Solution: 








M = +0' 


.016 = 


= 0" 


.002. 












C = +I 


.013. 






p. 


6. unit 


weight 


±0' 


'.018 


7r = +0' 


.073 = 


±=0" 


.009. 



B. D. + 24°4533- ' Pegasi. (22h2'M, + 24° 51'.) 
Mag. 3.96. //=+ o* .0220; +0." 018. Spectrum F5. 

The measures were made in longitude. The star is a spectro- 
scopic binary. No other parallax of this star has been published. 

Table i. 



No. 


Date 


Hour 
angle 


Observer 


No. of 
expo- 
sures 


Quality of 
images 


No. of 
inter- 
ferometer 


2 

3 


Oct. 19, 1914 
Nov. 16, 1914 
Nov. 18, 1914 


hr. min. 

-0 9 

10 

+ 18 


P. 
P. 
P. 


3 
3 
3 


2 
3 
5 


I 



4 
5 
6 

7 
8 

9 


June 28, 1915 
July 5, 1915 
July 6, 19 15 
July 8, 1915 
July 14, 1915 
July 17, 1915 


+0 4 
5 

■ 15 
5 

-0 43 

+0 


Ma. 

Ma. 

M. 

M. 

Ma. 

M. 


3 
3 
3 
3 
3 
3 


5 
3 
5 
4 
5 
4 










10 
II 
12 


Oct. 30, 1915 
Nov. 6, 1915 
Nov. 7, 1915 


+ 1 6 
40 
33 


Ma. 
Ma. 
S. 


2 
2 
3 


3 
4 

4 




I 



Table 2. 








COMPARISON 


STARS. 






No. 


X 


F 


Depend- 
ence 


Diameter 


B. D. No. 


Mag- 
nitude 


4 

7 
8 

13 

TT 


-147-588 
230.907 

+177-581 

200.915 

19.052 


+ 65.622 

- 26.866 

166.886 

+ 128.128 

12.199 


0.246 
0.210 
0.231 
0.313 


0.52 

0-43 
0.79 

0.34 
0.55 


+ 24° 4529 
24° 4536 


8-7 
8.3 



Normal equations: 



Solution: 



p. e. unit weight 



9.80OC+ o.479^t+o.6507r= —0.689. 
+ 15-593 +2.401 =+0.311. 
+7.068 =+0.096. 
yu = +o".094 ± o".oo7. 
c= — o .072. 
7r = +0^.063 ±o".oii. 

0".027. 



94 



JOHN A. MILLER 



B.D. + 56°274i. eCephei. (22^ iim.3^ _|_ 55° 33'.) 
Mag. 4.23. /x = +o^o544; +o".o44. Spectrum A5. 

The measures were made in longitude. This star has a large 
proper motion. Two other determinations of its parallax have 
been published. They are : 

By Smith ( HeHometer), who obtained + o".ioo. 

By Slocum and Mitchell (Photography), who obtained 
+ o".o6o. 

Table i. 

















Ac. of 




Xo. of 










Hour 




j expo- 


Qualitv of 


inter- 


No. 




Date 


; 


angle 


Observer 


sures 


images 


polations 










hr. 


mill. 




1 






I 


Oct. 


5, 


1913 


— 


10 


iM. 


3 


3 


2 


k 2 


Nov. 


3. 


1913 





5 


S. 


3 


5 





1 3 


Nov. 


2, 


1914 


+ 


1 


P. 


3 


3 





4 

5 


Nov. 


16, 


1914 





15 


P. 


3 


3 





.Tuly 


5, 


1915 


+ 


36 


Ma. 


2 


5 





6 


.hiiy 


8, 


1915 





20 


M. 


2 


4 





7 


Julv 


14. 


1915 








Ma. 


3 


5 





8 


Julv 


17. 


1915 





20 


M. 


3 


5 





9 


Julv 


22, 


1915 


—0 


7 


P. 


3 


5 





10 


July 


23. 


1915 


+ 


5 


Ma. 


3 


5 


I 


II 


Nov. 


20, 


1915 


+ 


27 


Ma. 


2 


4 





12 


Dec. 


4. 


19 15 





28 


Ma. 


2 


4 


I 



Table 





Weight 


lime m 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


CP) 


(m) 


(v) 


by 


I 


.8 


-5-24 


— 0.406 


-0.038 


.004 


M. 


2 


•9 


4-95 


.790 


•037 


.001 


M. 


3 


•7 


-I-3I 


-0.776 


.052 


.008 


M. 


4 


.7 


1. 17 


.900 


.068 


.006 


M. 


5 


.6 


+ 1.14 


+0.921 


.126 


.009 


M. 


6 


•7 


1. 17 


.898 


.127 


.009 


M. 


7 


I.O 


1-23 


•845 


•139 


.003 


M. 


8 


I.O 


1.26 


.815 


.144 


.007 


M. 


9 


•9 


I-3I 


.762 


.146 


.008 


M. 


10 


•9 


1.32 


•751 


.136 


.003 


M. 


II 


.8 


+2.52 


-0.925 


.161 


.002 


M. 


12 


•7 


2.66 


•979 


.162 


,001 


M. 



DEIERMINATION OF PARALLAXES OF FIFTY STARS 95 



COMPARISON STARS. 









Depend- 






Mag- 


No. 


X 


Y 


ence 


Diameter 


B. D. No. 


nitude 


2 


+221.098 


-100.854 


0.167 


0.33 


+ 56° 2748 


9-5 


7 


— 9.102 


+ 116.327 


O.161 


0.37 


56° 2745 


9-4 ; 


8 


75-658 


107.052 


0.185 


0.46 


56° 2738 


8.8 


10 


191. 611 


74-434 


0.233 


0.30 






12 


+ 55-273 


-196.957 


0.254 


0.42 


56° 2740 


9-3 


IT 


- 8.999 


1 1. 0^1 




0.45 







Normal equations: 



Solution : 



9.700c— 0.145^^+0.570^=0.964. 

+64.162 +8.205 =1.723. 

+6.520 =0.314. 



.003. 



p. e. unit weight ±o".oi9. 



+o".i23±o' 

+0 .099. 

+0". 030 ±0". 008. 



B. D. + 74° 1006. - Cephei. (23^4^.7, + 74° 51'.) 
Mag. 4.56. M = + 0^.0030 ; — o".025. Spectrum G5. 

The measures are in right ascension. This is a binary of 
long period. The combined image of the two images did not 
appear elongated and was bisected in making the measures. No 
other parallax of this star has been published. 

Table i. 



No. 


Date 


Hour 
angle 


Observer 


No. of 
expo- 
sures 


Quality of 
images 


No. of 
inter- 
polations 


I 
2 


Oct. 19, 1914 
Nov. 18, 1914 


hr. min. 
+ 

-0 3 


M. 
P. 


3 

3 


I 

5 


I 



3 
4 
5 
6 

7 


July 14, 1915 
July 17, 1915 
July 22, 19 15 
July 22,, 1915 
July 24, 1915 


+0 2 

20 

— 22 

+0 

6 


Ala. 

M. 

P. 

Ma. 
M. 


2 

2 

3 ' 

3 

3 


t 

4 
4 
4 









8 

9 
10 
II 

12 


Oct. 24, 1915 
Oct. 29, 1915 
Nov. 7, 1915 
Nov. 27, 1915 
Nov. 28, 1915 


+0 45 
34 
-0 25 
+0 26 
-0 25 


M. 
M. 

S. 
Ma. 

S. 


3 
2 

i 


3 

2 

4 
4 
4 












96 



JOHN A. MILLER 



Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 daj-s 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(v) 


by 


I 


•5 


-2.78 


— 0.61 


— 0.072 


— .002 


P. 


2 


.9 


2.48 


.86 


.067 


.001 


P. 


3 


I.O 


— O.IO 


+0.75 


.078 


.012 


P. 


4 


•5 


.07 


0.72 


•059 


.007 


P. 


5 


.6 


.02 


0.67 


.062 


.004 


P. 


6 


1.0 


.01 


0.66 


- .069 


.003 


P. 


7 


•5 


.00 


0.65 


•045 


.021 


P. 


8 


.6 


+0.92 


— 0.65 


.046 


.Oil 


P. 


9 


1.0 


•97 


.70 


.062 


.006 


P. 


10 


1.06 


•79 


0.60 


.004 


P. 


II 


1.0 


1.26 


.90 


0.48 


.006 




12 


.6 


1.27 


.90 


0.60 


.006 


P. 



COMPARISOX STARS. 









Depend- 






Mag- 


No. 


X 


Y 


ence 


Diameter 


B. D. No. 


nitude 


2 


+161.058 


— 162.988 


+ 0.255 


0.66 


+74° lOIO 


9^5 


4 


-213.488 


+ 42.090 


.281 


0.69 


74° 1000 


9-1 


6 


79.802 


105.798 


.242 


0.66 


74° 1003 


9-3 


10 


+132.232 


15.100 


.222 


0.50 






TV 


- 8.944 


- 0.698 




I. II 







Normal equations: 



Solution: 



9.1001:+ 0.728,u— I.8327r= — 0.561. 

14.446 -0.975 =+0.012. 

5.204 =+0.089. 



M=+0' 


.017^0' 


.007 


C = —0 


.063. 




7r= — 0' 


'.020 ±0' 


.012 



e. unit weio;ht ±o".026. 



B.D. + 56°2966. Bradley 3077. (23^^ 8-.5, + 56° 37'.) 
Alag. 5.65. M = + o^2522; +o".296. Spectrum K. 

The measures were in longitude. This star has a large proper 
motion. Brunnow, Blacklund, Gylden. Peters, and Flint have 
published parallaxes of this star. They found it, respectively, 
to be ^ o".o70, + o".20, + o".28. + o".i3, and + o".35. Adams 
found a hypothetical parallax for it of + o".!/.' 



DETERMIXAFJOX OF PARALLAXES OP FIPTY STARS 97 



Table i, 



No. 


Date 


Hour 
angle 


Observer 


No. of 
expo- 
sures 


Quality of 
images 


No. of 

inter- 
polations 


I 
2 

3 
4 


July i6, 1912 
July 26, 1912 
July 30, 19 12 
Oct. 5, 19 12 


hr. mill. 

+0 



-0 18 

20 


M. 
B. 
B. 
M. 


3 

2 

3 
2 


2 
2 
2 

5 


4 


3 



5 
6 

7 


Oct. 16, 1912 
Oct. 20, 1912 
Nov. 19, 1912 


-0 6 

25 

+ 


B. 


I 

I 


4 
3 
4 




I 


8 
9 

10 


July 8, 1913 
July II, 19 13 
Oct. 5, 1913 


+0 30 

-0 35 

15 


B. 

S. 
M. 


2 
3 
3 


5 
4 
3 



I 



II 

12 

13 


Oct. 16, 1913 
Nov. I, 1913 
Nov. 4, 1913 


— 14 
+0 15 

-0 15 




3 
3 
3 


5 
5 
4 




2 
2 


14 

15 


Aug. 13, 1914 
Aug. 16, 1914 


+0 30 
30 


P. 
P. 


2 
2 


4 
I 




I 



Table 2. 





Weight 


Time in 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(v) 


by 


I 


•7 


-3.00 


+ I.OI6 


— 0.261 


.002 


S. 


2 


•7 


2.90 


0.995 


.247 


.002 


S. 


3 


.6 


2.86 


•979 


.248 


.004 


M. 


4 


.6 


2.19 


.171 


.203 


•005 


S. 


5 


.5 


-2.08 


— 0.018 


.201 


.008 


S. 


6 


•7 


2.04 


.086 


.183 


.008 


M. 


7 


•7 


1.74 


.566 


.179 


.004 


S. 


8 


•7 


+0.57 


+ 1.011 


+ 0.146 


.006 


M. 


9 


•9 


0.60 


1.015 


.165 


.010 


M. 


10 


•7 


1.46 


0.175 


.220 


.002 


S. 


II 


•7 


+1.57 


-0.013 


•236 


.009 


S. 


12 


.8 


1-73 


.285 


.236 


.001 


S. 


13 


.6 


1.76 


•334 


.236 


.001 


s. 


14 


•7 


+4-58 


+0.892 


.606 


.002 


p. 


15 


.8 


4.61 


.866 


.607 


.004 


p. 



COMPARISOX STARS. 









Depend- 






Mag- 


No. 


X 


y 


ence 


Diameter 


B. D. Xo. 


nitude 


2 


+ 109.451 


+ 74-243 


0.20 


0.58 






6 


- 47-972 


165.201 


0.18 


0.68 






8 


81.336 


161.904 


0.17 


0.56 






9 


167-544 


— 63.150 


0.12 


0.74 






II 


+ 122.059 


103-443 


0.18 


0-75 


+ 56° 2970 


9.1 


13 


65-343 


234-753 


0.15 


0.57 






TV 


II -3 15 


+ 10.637 




0.T8 







Normal equations: 



Solution: 



p. e. unit weight 



67.189M+ i.368c + i.2867r = 7.848. 

+ 10.508 +4.201 =0.813. 

+ 5.226 =0.547. 

M = +0". 540=^0". 002. 

^ = +0 .047. 

7r=+o".l8l ±o".009. 



B. D. + 26°4734. 85 Pegasi =^ 733. 23^^56^.8, + 26° 34'.; 
Alag. 5.85. yu = + 0^0622; — o".986. Spectrum G. 

The measures were made in longitude. This is a binary of 
26.3 years. The faint component did not affect the image of 
the brighter one. Brunnow. Fhnt, Chase, Slocum, and jMitchell 
have pubhshed parahaxes of this star. They are, respectively, 
+ o".o54, + o".03, + o".io, and + o.''o84. Adams and Russell give 
hypothetical parallaxes for this star of + o".io and + ©".O/i 
respectively. 

Table i. 



No. 


Date 


Hour 
angle 


Observer 


No. of 
expo- 
sures 


Quality of 
images 


No. of 
inter- 
polations 


I 
2 


July 22, 1912 
July 30, 19 1 2 


hr. mill. 
+ 36 
-0 18 


B. 
B. 


2 
2 


4 

4 


I 



3 
4 


Nov. 18, 19 12 

Nov. 19, 19 12 


-0 24 

+ 


B. 

M. 


3 
3 


5 
4 




I 


5 
6 

7 
8 

9 


Oct. 15, 1913 
Oct. 16, 1913 

Oct. 22, I913 
Nov. 22, I9I3 

Dec. II, 1913 


+ 12 
17 

17 

1 
— 10 


P. 
M. 
P. 
M. 

M. 


3 
3 
3 
3 
3 


2 
5 
5 
4 

4 




I 






10 
II 
12 
13 
14 
15 
16 


July 19, 1914 
July 28, 1914 
July 29, 19 14 
July 31. 19 14 
Aug. 15, 1914 
Aug. 16, 1914 
Aug. 21, 1914 


-0 8 

+0 20 

-0 15 

+0 35 

I 

36 

46 


S. 

S. 

S. 

M. 

P. 

P. 

P. 


2 
3 
3 
3 
3 
2 

3 


5 
4 
5 
4 
5 
2 

4 






I 







DETERMINATION OF PARALLAXES OF FIFTY STARS 99 



Table 2. 





Weight 


Time m 


Parallax 










of plate 


100 days 


factor 


Solution 


Residual 


Measured 


No. 


(P) 


(T) 


(P) 


(m) 


(V) 


by 


I 


.8 


-4.88 


+0.961 


+ I.912 


.005 


P. 


2 


.8 


4.80 


.908 


1.924 


.008 


P. 


3 


•7 


-3-69 


— 0.700 


I.9IO 


.004 


P. 


4 


•9 


3.68 


.712 


1.897 


.010 


P. 


5 


.9 


-0.38 


-0.189 


1.984 


.005 


H. 


6 


•9 


0.37 


.206 


1-993 


.004 


P. 


7 


•9 


0.31 


.306 


1.992 


.005 


P. 


8 


.8 


0.00 


.647 


1.982 


.005 


P. 


9 


•9 


+0.19 


.914 


1. 99 1 


.006 


P. 


10 


•7 


+2.39 


+0.979 


2.078 


.004 


P. 


II 


I.O 


2.48 


.926 


2.070 


.005 


H. 


12 


•5 


2.49 


.914 


2.081 


.006 


P. 


13 


•7 


2.51 


.904 


2.067 


.008 


M. 


14 


.9 


2.66 


.760 


2.073 


.001 


H. 


15 


.8 


2.67 


.748 


2.085 


.010 


P. 


16 


1.0 


2.72 


.688 


2.070 


.005 


P. 



COMPARISON STARS. 









Depend- 






Mag- 


No. 


A- 


r 


ence 


Diameter 


B. D. No. 


nitude 


I 


- 9427 


+ 166.808 


0.25 


0.44 






2 


117. 716 


172.553 


0.25 


0.40 


+ 26° 4732 


9.5 


5 


166.681 


— 211. 761 


0.24 


0.42 






8 


+293.822 


127.601 


0.26 


0.44 






TT 


6.594 


+ 0.396 




0.72 







Normal equations 



Solution: 



96.685/x- o.oi4c+8.9577r= 2.254. 

+ 13.205 +3.068 = 26.483. 

+7.402 = 6.491. 



e. unit weight — o".oi9. 



+o".ioi 
+ 2 .001 
+o".ioi 



= o".oo8.